TY  - JOUR
A1  - Azzali, Sara
A1  - Goette, Sebastian
A1  - Schick, Thomas
T1  - Large time limit and local L-2-index theorems for families
JF  - Journal of noncommutative geometry
N2  - We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L-2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined L-2-index formulas.
 As applications, we prove a local L-2-index theorem for families of signature operators and an L-2-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tondeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct L-2-eta forms and L-2-torsion forms as transgression forms.
KW  - Local index theory
KW  - eta forms
KW  - torsion forms
KW  - L-2-invariants
Y1  - 2015
U6  - https://doi.org/10.4171/JNCG/203
SN  - 1661-6952
SN  - 1661-6960
VL  - 9
IS  - 2
SP  - 621
EP  - 664
PB  - EMS Publ.
CY  - Zürich
ER  - 
TY  - JOUR
A1  - Schick, Thomas
A1  - Seyedhosseini, Mehran
T1  - On an index theorem of Chang, Weinberger and Yu
JF  - Münster journal of mathematics
N2  - In this paper we prove a strengthening of a theorem of Chang, Weinberger and Yu on obstructions to the existence of positive scalar curvature metrics on compact manifolds with boundary. They construct a relative index for the Dirac operator, which lives in a relative K-theory group, measuring the difference between the fundamental group of the boundary and of the full manifold. 
Whenever the Riemannian metric has product structure and positive scalar curvature near the boundary, one can define an absolute index of the Dirac operator taking value in the K-theory of the C*-algebra of fundamental group of the full manifold. This index depends on the metric near the boundary. We prove that (a slight variation of) the relative index of Chang, Weinberger and Yu is the image of this absolute index under the canonical map of K-theory groups.
This has the immediate corollary that positive scalar curvature on the whole manifold implies vanishing of the relative index, giving a conceptual and direct proof of the vanishing theorem of Chang, Weinberger and Yu (rather: a slight variation). To take the fundamental groups of the manifold and its boundary into account requires working with maximal C*-completions of the involved *-algebras. A significant part of this paper is devoted to foundational results regarding these completions. On the other hand, we introduce and propose a more conceptual and more geometric completion, which still has all the required functoriality.
Y1  - 2021
U6  - https://doi.org/10.17879/59019522628
SN  - 1867-5778
SN  - 1867-5786
VL  - 14
IS  - 1
SP  - 123
EP  - 154
PB  - WWU, Fachbereich Mathematik und Informatik
CY  - Münster
ER  - 
TY  - JOUR
A1  - Schick, Daniel
A1  - Le Guyader, Loic
A1  - Pontius, Niko
A1  - Radu, Ilie
A1  - Kachel, Torsten
A1  - Mitzner, Rolf
A1  - Zeschke, Thomas
A1  - Schuessler-Langeheine, Christian
A1  - Föhlisch, Alexander
A1  - Holldack, Karsten
T1  - Analysis of the halo background in femtosecond slicing experiments
JF  - Journal of synchrotron radiation
N2  - The slicing facility FemtoSpeX at BESSY II offers unique opportunities to study photo-induced dynamics on femtosecond time scales by means of X-ray magnetic circular dichroism, resonant and non-resonant X-ray diffraction, and X-ray absorption spectroscopy experiments in the soft X-ray regime. Besides femtosecond X-ray pulses, slicing sources inherently also produce a so-called `halo' background with a different time structure, polarization and pointing. Here a detailed experimental characterization of the halo radiation is presented, and a method is demonstrated for its correct and unambiguous removal from femtosecond time-resolved data using a special laser triggering scheme as well as analytical models. Examples are given for time-resolved measurements with corresponding halo correction, and errors of the relevant physical quantities caused by either neglecting or by applying a simplified model to describe this background are estimated.
KW  - femtosecond slicing
KW  - halo
KW  - pump-probe
KW  - XMCD
KW  - X-ray scattering
Y1  - 2016
U6  - https://doi.org/10.1107/S160057751600401X
SN  - 1600-5775
VL  - 23
SP  - 700
EP  - 711
PB  - International Union of Crystallography
CY  - Chester
ER  -