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  -