The index formula for families of Dirac type operators on pseudomanifolds

TL;DR

This paper develops an index formula for families of Dirac operators on stratified pseudomanifolds with wedge metrics, establishing their analytical properties and computing their Chern character.

Contribution

It introduces a framework for analyzing Dirac families on stratified spaces and derives an explicit index formula under invertibility assumptions.

Findings

Operators are self-adjoint and Fredholm with compact resolvents.

Established trace-class heat kernels for the operators.

Derived a formula for the Chern character of their index.

Abstract

We study families of Dirac-type operators, with compatible perturbations, associated to wedge metrics on stratified spaces. We define a closed domain and, under an assumption of invertible boundary families, prove that the operators are self-adjoint and Fredholm with compact resolvents and trace-class heat kernels. We establish a formula for the Chern character of their index.