Volterra calculus, local equivariant family index theorem and equivariant eta forms

Abstract

In this paper, we give proofs of the family index formula and the equivariant family index formula by the Greiner's approach to heat kernel asymptotics. We compute equivariant family JLO characters. We also define the equivariant eta form and give a proof of its regularity.

29 pages, to appear in The Asian Journal of Mathematics

References in corpus (2)

• Noncommutative geometry, conformal geometry, and the local equivariant index theorem
• Noncommutative Geometry and Conformal Geometry. II. Connes-Chern character and the local equivariant index theorem

Cited by in corpus (4)

• Functoriality of equivariant eta forms
• The Greiner's approach to heat kernel asymptotics and the variation formulas for the equivariant Ray-Singer metric
• The Noncommutative Infinitesimal Equivariant Index Formula
• The noncommutative family Atiyah-Patodi-Singer index theorem