@phdthesis{Becker2005,
  author    = {Becker, Christian},
  title     = {On the Riemannian geometry of Seiberg-Witten moduli spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-5425},
  school      = {Universit{\"a}t Potsdam},
  year      = {2005},
  abstract  = {In this thesis, we give two constructions for Riemannian metrics on Seiberg-Witten moduli spaces. Both these constructions are naturally induced from the L2-metric on the configuration space. The construction of the so called quotient L2-metric is very similar to the one construction of an L2-metric on Yang-Mills moduli spaces as given by Groisser and Parker. To construct a Riemannian metric on the total space of the Seiberg-Witten bundle in a similar way, we define the reduced gauge group as a subgroup of the gauge group. We show, that the quotient of the premoduli space by the reduced gauge group is isomorphic as a U(1)-bundle to the quotient of the premoduli space by the based gauge group. The total space of this new representation of the Seiberg-Witten bundle carries a natural quotient L2-metric, and the bundle projection is a Riemannian submersion with respect to these metrics. We compute explicit formulae for the sectional curvature of the moduli space in terms of Green operators of the elliptic complex associated with a monopole. Further, we construct a Riemannian metric on the cobordism between moduli spaces for different perturbations. The second construction of a Riemannian metric on the moduli space uses a canonical global gauge fixing, which represents the total space of the Seiberg-Witten bundle as a finite dimensional submanifold of the configuration space. We consider the Seiberg-Witten moduli space on a simply connected K\äuhler surface. We show that the moduli space (when nonempty) is a complex projective space, if the perturbation does not admit reducible monpoles, and that the moduli space consists of a single point otherwise. The Seiberg-Witten bundle can then be identified with the Hopf fibration. On the complex projective plane with a special Spin-C structure, our Riemannian metrics on the moduli space are Fubini-Study metrics. Correspondingly, the metrics on the total space of the Seiberg-Witten bundle are Berger metrics. We show that the diameter of the moduli space shrinks to 0 when the perturbation approaches the wall of reducible perturbations. Finally we show, that the quotient L2-metric on the Seiberg-Witten moduli space on a K\ähler surface is a K\ähler metric.},
  subject      = {Eichtheorie},
  language  = {en}
}
@misc{BeckerSchenkelSzabo2017,
  author    = {Becker, Christian and Schenkel, Alexander and Szabo, Richard J.},
  title     = {Differential cohomology and locally covariant quantum field theory},
  series = {Reviews in Mathematical Physics},
  volume    = {29},
  journal   = {Reviews in Mathematical Physics},
  number    = {1},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0129-055X},
  doi       = {10.1142/S0129055X17500039},
  pages     = {42},
  year      = {2017},
  abstract  = {We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr{\´e}chet-Lie group structure on differential cohomology groups.},
  language  = {en}
}
@article{BeckerBeniniSchenkeletal.2019,
  author    = {Becker, Christian and Benini, Marco and Schenkel, Alexander and Szabo, Richard J.},
  title     = {Cheeger-Simons differential characters with compact support and Pontryagin duality},
  series = {Communications in analysis and geometry},
  volume    = {27},
  journal   = {Communications in analysis and geometry},
  number    = {7},
  publisher = {International Press of Boston},
  address   = {Somerville},
  issn      = {1019-8385},
  doi       = {10.4310/CAG.2019.v27.n7.a2},
  pages     = {1473 -- 1522},
  year      = {2019},
  abstract  = {By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. We prove an excision theorem for differential cohomology using a suitable relative version. Furthermore, we use our model to give an independent proof of Pontryagin duality for differential cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125 (2003), 791]: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.},
  language  = {en}
}
@article{BaerBecker2014,
  author    = {B{\"a}r, Christian and Becker, Christian},
  title     = {Differential characters and geometric chains},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2112},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-07034-6; 978-3-319-07033-9},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-07034-6_1},
  pages     = {1 -- 90},
  year      = {2014},
  abstract  = {We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohomology theory and the model given by differential characters. Fiber integration for fibers with boundary is treated in the context of relative differential characters. As applications we treat higher-dimensional holonomy, parallel transport, and transgression.},
  language  = {en}
}
@article{Becker2014,
  author    = {Becker, Christian},
  title     = {Relative differential cohomology},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2112},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-07034-6; 978-3-319-07033-9},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-07034-6_2},
  pages     = {91 -- 180},
  year      = {2014},
  abstract  = {We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters.},
  language  = {en}
}
@article{Becker2016,
  author    = {Becker, Christian},
  title     = {Cheeger-Chern-Simons Theory and Differential String Classes},
  series = {Annales de l'Institut Henri Poincar{\~A}©},
  volume    = {17},
  journal   = {Annales de l'Institut Henri Poincar{\~A}©},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1424-0637},
  doi       = {10.1007/s00023-016-0485-6},
  pages     = {1529 -- 1594},
  year      = {2016},
  abstract  = {We construct new concrete examples of relative differential characters, which we call Cheeger-Chern-Simons characters. They combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary. We study the differential cohomology of compact Lie groups G and their classifying spaces BG. We show that the even degree differential cohomology of BG canonically splits into Cheeger-Simons characters and topologically trivial characters. We discuss the transgression in principal G-bundles and in the universal bundle. We introduce two methods to lift the universal transgression to a differential cohomology valued map. They generalize the Dijkgraaf-Witten correspondence between 3-dimensional Chern-Simons theories and Wess-Zumino-Witten terms to fully extended higher-order Chern-Simons theories. Using these lifts, we also prove two versions of a differential Hopf theorem. Using Cheeger-Chern-Simons characters and transgression, we introduce the notion of differential trivializations of universal characteristic classes. It generalizes well-established notions of differential String classes to arbitrary degree. Specializing to the class , we recover isomorphism classes of geometric string structures on Spin (n) -bundles with connection and the corresponding spin structures on the free loop space. The Cheeger-Chern-Simons character associated with the class together with its transgressions to loop space and higher mapping spaces defines a Chern-Simons theory, extended down to points. Differential String classes provide trivializations of this extended Chern-Simons theory. This setting immediately generalizes to arbitrary degree: for any universal characteristic class of principal G-bundles, we have an associated Cheeger-Chern-Simons character and extended Chern-Simons theory. Differential trivialization classes yield trivializations of this extended Chern-Simons theory.},
  language  = {en}
}
@article{Becker2007,
  author    = {Becker, Christian},
  title     = {Menschenrechte und Demokratie},
  series = {MenschenRechtsMagazin : MRM ; Informationen, Meinungen, Analysen},
  volume    = {12},
  journal   = {MenschenRechtsMagazin : MRM ; Informationen, Meinungen, Analysen},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1434-2820},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-36646},
  pages     = {283 -- 290},
  year      = {2007},
  abstract  = {I. Einleitung II. Anerkennung zwischen Universalisierung und Partikularisierung III. Die demokratische Praxis als Anerkennungsform IV. Selbstbegrenzung und Selbstentgrenzung},
  language  = {de}
}
@misc{AnlaufBeckerBilletetal.2007,
  author    = {Anlauf, Lena and Becker, Christian and Billet, Camille and Etzi, Priamo and Glienicke, Frank and Haghanipour, Bahar and Meyer, Gunda and Rießbeck, Sebastian and Volger, Helmut and Welke, Jenny and Wendt, Johannes},
  title     = {MenschenRechtsMagazin : Informationen │ Meinungen │ Analysen},
  volume    = {12},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1434-2820},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-36793},
  year      = {2007},
  abstract  = {• Menschenrechte und Demokratie • Hannah Arendt und das Recht, Rechte zu haben • Kindersoldaten aus v{\"o}lkerrechtlicher Perspektive - Teil II • Guant{\´a}namo Bay - ein rechtsfreier Raum? • Bericht {\"u}ber die Sitzungen des Menschenrechtsrates der Vereinten Nationen 2006/2007},
  language  = {de}
}
@book{AmbauenArnoldBeckeretal.2021,
  author    = {Ambauen, Ladina and Arnold, Maren and Becker, Christian and Chahrour, Mohamed Chaker and Destanovic, Edis and Fretter, Alexandra and Geißler, Marc and Gr{\"u}nberg, Uwe and Habl, Moritz and Hoffmann, Sandra and Juchler, Ingo and Jurkatis, Lena Christine and Keitel, Bernhard and Losensky, Nikolai and Mrowietz, Christian and Nadol, Dominic and Naumann, Asja and Ockenga, Imke and Pohlandt, Anne and P{\"u}rschel, Tobias and Recktenwald, Michelle and Stephan, Roswitha and Tuchel, Johannes and Weinkamp, Christina and Weiß, Christian and Wiecking, Ole and Wockenfuß, Patricia and Zalitatsch, Nora Lina},
  title     = {Mildred Harnack und die Rote Kapelle in Berlin},
  editor    = {Juchler, Ingo},
  edition   = {2., verbesserte Auflage},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-500-2},
  doi       = {10.25932/publishup-48176},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-481762},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {170},
  year      = {2021},
  abstract  = {Mildred Harnack, geb. Fish, stammte urspr{\"u}nglich aus Milwaukee, Wisconsin. Zusammen mit ihrem Ehemann Arvid Harnack zog sie nach Deutschland und lebte seit 1930 in Berlin. Hier lehrte die Literaturwissenschaftlerin an der Friedrich-Wilhelms-Universit{\"a}t (heute Humboldt-Universit{\"a}t) und am Berliner Abendgymnasium (heute Peter A. Silbermann-Schule). Bereits kurz nach der Macht{\"u}bernahme von Adolf Hitler hatte sich um das Ehepaar Harnack ein Kreis von Freunden gebildet, der gegen die Herrschaft der Nationalsozialisten opponierte. Dazu z{\"a}hlten auch Karl Behrens und Bodo Schl{\"o}singer, die beide Sch{\"u}ler Mildred Harnacks am Berliner Abendgymnasium waren. Mildred Harnack konnte mit Hilfe ihrer Kontakte zur amerikanischen Botschaft ihren Sch{\"u}lern im nationalsozialistischen Deutschland ansonsten nicht zug{\"a}ngliche Informationen besorgen. Aufgrund von Funkkontakten des Freundeskreises zur Sowjetunion wurde die Gruppe von den Nationalsozialisten Rote Kapelle genannt - „rot" bezog sich auf deren linke Haltung und mit „Kapelle" wurden Funker assoziiert, die wie Pianisten in einer Kapelle spielen. Der Berliner Oppositionszirkel umfasste bis zu seiner Zerschlagung durch die Nationalsozialisten etwa 150 Personen verschiedenster Berufsgruppen, unterschiedlicher parteipolitischer Einstellungen und Konfessionen. Die Gruppe verfertigte oppositionelle Flugbl{\"a}tter und lieferte Informationen an die amerikanische Botschaft sowie an die Sowjetunion. Mildred Harnack wurde - wie viele ihrer Mitstreiterinnen und Mitstreiter - nach ihrer Verhaftung vom Reichskriegsgericht zum Tode verurteilt und am 16. Februar 1943 in Pl{\"o}tzensee guillotiniert. In diesem Band stellen Studierende der Universit{\"a}t Potsdam sowie H{\"o}rerinnen und H{\"o}rer der Peter A. Silbermann-Schule (Berlin) nach einem kurzen {\"U}berblick zum Widerstand gegen den Nationalsozialismus in Deutschland das Netzwerk der Roten Kapelle sowie die Biographien von Mildred Harnack und ihren Sch{\"u}lern Karl Behrens und Bodo Schl{\"o}singer vom Berliner Abendgymnasium eindr{\"u}cklich vor.},
  language  = {de}
}
@book{AmbauenArnoldBeckeretal.2017,
  author    = {Ambauen, Ladina and Arnold, Maren and Becker, Christian and Chahrour, Mohamed Chaker and Destanovic, Edis and Fretter, Alexandra and Geißler, Marc and Gr{\"u}nberg, Uwe and Habl, Moritz and Hoffmann, Sandra and Juchler, Ingo and Jurkatis, Lena Christine and Keitel, Bernhard and Losensky, Nikolai and Mrowietz, Christian and Nadol, Dominic and Naumann, Asja and Ockenga, Imke and Pohlandt, Anne and P{\"u}rschel, Tobias and Recktenwald, Michelle and Stephan, Roswitha and Tuchel, Johannes and Weinkamp, Christina and Weiß, Christian and Wiecking, Ole and Wockenfuß, Patricia and Zalitatsch, Nora Lina},
  title     = {Mildred Harnack und die Rote Kapelle in Berlin},
  editor    = {Juchler, Ingo},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-407-4},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-398166},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {170},
  year      = {2017},
  abstract  = {Mildred Harnack, geb. Fish, stammte urspr{\"u}nglich aus Milwaukee, Wisconsin. Zusammen mit ihrem Ehemann Arvid Harnack zog sie nach Deutschland und lebte seit 1930 in Berlin. Hier lehrte die Literaturwissenschaftlerin an der Friedrich-Wilhelms-Universit{\"a}t (heute Humboldt-Universit{\"a}t) und am Berliner Abendgymnasium (heute Peter A. Silbermann-Schule). Bereits kurz nach der Macht{\"u}bernahme von Adolf Hitler hatte sich um das Ehepaar Harnack ein Kreis von Freunden gebildet, der gegen die Herrschaft der Nationalsozialisten opponierte. Dazu z{\"a}hlten auch Karl Behrens und Bodo Schl{\"o}singer, die beide Sch{\"u}ler Mildred Harnacks am Berliner Abendgymnasium waren. Mildred Harnack konnte mit Hilfe ihrer Kontakte zur amerikanischen Botschaft ihren Sch{\"u}lern im nationalsozialistischen Deutschland ansonsten nicht zug{\"a}ngliche Informationen besorgen. Aufgrund von Funkkontakten des Freundeskreises zur Sowjetunion wurde die Gruppe von den Nationalsozialisten Rote Kapelle genannt - „rot" bezog sich auf deren linke Haltung und mit „Kapelle" wurden Funker assoziiert, die wie Pianisten in einer Kapelle spielen. Der Berliner Oppositionszirkel umfasste bis zu seiner Zerschlagung durch die Nationalsozialisten etwa 150 Personen verschiedenster Berufsgruppen, unterschiedlicher parteipolitischer Einstellungen und Konfessionen. Die Gruppe verfertigte oppositionelle Flugbl{\"a}tter und lieferte Informationen an die amerikanische Botschaft sowie an die Sowjetunion. Mildred Harnack wurde - wie viele ihrer Mitstreiterinnen und Mitstreiter - nach ihrer Verhaftung vom Reichskriegsgericht zum Tode verurteilt und am 16. Februar 1943 in Pl{\"o}tzensee guillotiniert. In diesem Band stellen Studierende der Universit{\"a}t Potsdam sowie H{\"o}rerinnen und H{\"o}rer der Peter A. Silbermann-Schule (Berlin) nach einem kurzen {\"U}berblick zum Widerstand gegen den Nationalsozialismus in Deutschland das Netzwerk der Roten Kapelle sowie die Biographien von Mildred Harnack und ihren Sch{\"u}lern Karl Behrens und Bodo Schl{\"o}singer vom Berliner Abendgymnasium eindr{\"u}cklich vor.},
  language  = {de}
}