Large time limit and local L-2-index theorems for families

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.

Metadaten
Author details:	Sara Azzali ORCiD, Sebastian Goette, Thomas Schick
DOI:	https://doi.org/10.4171/JNCG/203
ISSN:	1661-6952
ISSN:	1661-6960
Title of parent work (English):	Journal of noncommutative geometry
Publisher:	EMS Publ.
Place of publishing:	Zürich
Publication type:	Article
Language:	English
Year of first publication:	2015
Publication year:	2015
Release date:	2017/03/27
Tag:	L-2-invariants; Local index theory; eta forms; torsion forms
Volume:	9
Issue:	2
Number of pages:	44
First page:	621
Last Page:	664
Funding institution:	INdAM-Cofund fellowship; German Research Foundation (DFG) through the Institutional Strategy of the University of Gottingen; DFG special programme "Global Differential Geometry"; DFG-SFB TR "Geometric Partial Differential Equations"; Courant Research Center "Higher order structures in Mathematics" within the Gelman initiative of excellence
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer review:	Referiert