Simple homotopy invariance of higher signatures

TL;DR

This paper proves that higher signatures are invariant under simple homotopy equivalences for closed oriented manifolds, establishing a fundamental property in geometric topology.

Contribution

It demonstrates that higher signatures are invariant under simple homotopy, extending their known invariance properties in topology.

Findings

Higher signatures are simple-homotopy invariants.

The invariance holds for all closed oriented manifolds.

Abstract

We prove that the higher signature for any close oriented manifold is a simple-homotopy invariant.