The symmetric signature of a Witt space

TL;DR

This paper introduces a new construction of the symmetric signature for Witt spaces, extending the concept of self-duality in intersection homology to a broader class of singular spaces, with properties akin to those for manifolds.

Contribution

It provides a novel symmetric signature construction for Witt spaces, similar to Miscenko's for manifolds, with invariance under stratified homotopy equivalence.

Findings

Construction has all expected properties

Invariance under stratified homotopy equivalence

Extends symmetric signature to Witt spaces

Abstract

Witt spaces are pseudomanifolds for which the middle-perversity intersection homology with rational coefficients is self-dual. We give a new construction of the symmetric signature for Witt spaces which is similar in spirit to the construction given by Miscenko for manifolds. Our construction has all of the expected properties, including invariance under stratified homotopy equivalence.