期刊
JOURNAL OF NONCOMMUTATIVE GEOMETRY
卷 9, 期 2, 页码 621-664出版社
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JNCG/203
关键词
Local index theory; eta forms; torsion forms; L-2-invariants
资金
- 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
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.
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