Functoriality of equivariant eta forms

TL;DR

This paper introduces the equivariant eta form for compact Lie groups and proves a functoriality formula related to the composition of submersions, advancing the understanding of equivariant index theory.

Contribution

It defines the equivariant eta form for compact Lie groups and establishes a functoriality formula for compositions of submersions, extending previous theoretical frameworks.

Findings

Defined the equivariant eta form for compact Lie groups

Proved a functoriality formula for composed submersions

Enhanced the theoretical understanding of equivariant index theory

Abstract

In this paper, we define the equivariant eta form of Bismut-Cheeger for a compact Lie group and establish a formula about the functoriality of equivariant eta forms with respect to the composition of two submersions.