TY - JOUR A1 - Roos, Saskia T1 - The Dirac operator under collapse to a smooth limit space JF - Annals of global analysis and geometry N2 - Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B. KW - Collapse KW - Dirac operator KW - Spin geometry Y1 - 2019 U6 - https://doi.org/10.1007/s10455-019-09691-8 SN - 0232-704X SN - 1572-9060 VL - 57 IS - 1 SP - 121 EP - 151 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Ludewig, Matthias A1 - Roos, Saskia T1 - The chiral anomaly of the free fermion in functorial field theory JF - Annales Henri Poincaré : a journal of theoretical and mathematical physics N2 - When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules. Y1 - 2020 U6 - https://doi.org/10.1007/s00023-020-00893-6 SN - 1424-0637 SN - 1424-0661 VL - 21 IS - 4 SP - 1191 EP - 1233 PB - Springer International Publishing AG CY - Cham (ZG) ER - TY - JOUR A1 - Roos, Saskia A1 - Otoba, Nobuhiko T1 - Scalar curvature and the multiconformal class of a direct product Riemannian manifold JF - Geometriae dedicata N2 - For a closed, connected direct product Riemannian manifold (M, g) = (M-1, g(1)) x ... x (M-l, g(l)), we define its multiconformal class [[g]] as the totality {integral(2)(1)g(1) circle plus center dot center dot center dot integral(2)(l)g(l)} of all Riemannian metrics obtained from multiplying the metric gi of each factor Mi by a positive function fi on the total space M. A multiconformal class [[ g]] contains not only all warped product type deformations of g but also the whole conformal class [(g) over tilde] of every (g) over tilde is an element of[[ g]]. In this article, we prove that [[g]] contains a metric of positive scalar curvature if and only if the conformal class of some factor (Mi, gi) does, under the technical assumption dim M-i = 2. We also show that, even in the case where every factor (M-i, g(i)) has positive scalar curvature, [[g]] contains a metric of scalar curvature constantly equal to -1 and with arbitrarily large volume, provided l = 2 and dim M = 3. KW - Positive scalar curvature KW - Constant scalar curvature KW - The Yamabe KW - problem KW - Warped product KW - Umbilic product KW - Twisted product Y1 - 2021 U6 - https://doi.org/10.1007/s10711-021-00636-9 SN - 0046-5755 SN - 1572-9168 VL - 214 IS - 1 SP - 801 EP - 829 PB - Springer CY - Dordrecht ER - TY - BOOK A1 - Schubarth, Wilfried A1 - Zylla, Birgitta A1 - Niproschke, Saskia A1 - Guder, Petra A1 - Sonnen, Bernd-Rüdeger A1 - Kahl, Wolfgang A1 - Groeger-Roth, Frederick A1 - Kaeding, Peer A1 - Böhm, Christian A1 - Voigt, Jana A1 - Sturzbecher, Dietmar A1 - Kohlstruck, Michael A1 - Möller, Kurt A1 - Rolfes, Manfred A1 - Winter, Frank A1 - Breitschwerdt, Michael A1 - Kopp, Andrea A1 - Hinze, Klaus A1 - Lösel, Friedrich A1 - Klindworth-Mohr, Antje A1 - Madl, Martina A1 - Dunand, Annelie A1 - Schanzenbächer, Stefan A1 - Rump-Räuber, Michael A1 - Roos, Alfred A1 - Seidel, Andreas A1 - Gröger, Ulli A1 - Ulbricht, Juliane A1 - Martin, Christian A1 - Behrendt, Daniel ED - Schubarth, Wilfried T1 - Nachhaltige Prävention von Kriminalität, Gewalt und Rechtsextremismus BT - Beiträge aus Wissenschaft und Praxis N2 - Was wird unter „nachhaltiger Prävention“ in der Präventionsforschung verstanden? Welche guten Beispiele für nachhaltige Prävention gibt es in der Praxis? Und v. a.: Wie lässt sich Prävention in den verschiedenen Bereichen wie Kriminalität, Gewalt und Rechtsextremismus nachhaltig gestalten? Diesen Fragen will der vorliegende Sammelband nachgehen und damit der Präventionsdebatte neue Impulse verleihen. Der Band will insbesondere die nationale sowie internationale Fachdebatte konstruktiv aufgreifen, Theorie und Praxis verbinden, „good practice“ Beispiele darstellen sowie Perspektiven nachhaltiger Prävention aufzeigen. Mit diesem Themenspektrum richtet er sich sowohl an die Wissenschaft als auch an die Praxis sowie insgesamt an eine interessierte Öffentlichkeit. N2 - What is meant by „sustainable prevention“ in prevention research? What are good examples for sustainable prevention? And above all: How can prevention in fields like crime, violence and right-wing extremism be arranged sustainably? This miscellany is focused on these questions and it is intend to give new inputs for the current discussion on sustainable prevention. Especially, the miscellany is meant to connect the national and international trade debate, to combine theory and practice, to describe examples of “good practice” as well as to show prospects of sustainable prevention. These range of topics focus on science and practice as well as an interested public in general. KW - Prävention KW - Nachhaltigkeit KW - Gewalt KW - Kriminalität KW - Rechtsextremismus KW - prevention KW - sustainability KW - violence KW - crime KW - right-wing extremism Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70537 SN - 978-3-86956-014-4 PB - Universitätsverlag Potsdam CY - Potsdam ER -