Large time limit and local L2L^2-index theorems for families

  • Sara Azzali

    Universität Potsdam, Germany
  • Sebastian Goette

    Universität Freiburg, Germany
  • Thomas Schick

    Georg-August-Universität Göttingen, Germany


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 L2L^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 L2L^2-index formulas.

As applications, we prove a local L2L^2-index theorem for families of signature operators and an L2L^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 L2L^2-eta forms and L2L^2-torsion forms as transgression forms.

Cite this article

Sara Azzali, Sebastian Goette, Thomas Schick, Large time limit and local L2L^2-index theorems for families. J. Noncommut. Geom. 9 (2015), no. 2, pp. 621–664

DOI 10.4171/JNCG/203