On cut-and-Past invariance of Kervaire semi-characteristic

TL;DR

This paper proves that the relative Kervaire semi-characteristic remains invariant under cut-and-paste operations using an analytic approach inspired by W. Zhang.

Contribution

It introduces a new analytic method to establish the invariance of the relative Kervaire semi-characteristic under cut-and-paste transformations.

Findings

Invariance of the relative Kervaire semi-characteristic under cut-and-paste

Application of analytic techniques to topological invariants

Extension of Zhang's method to this context

Abstract

In this note we study the relative Kervaire semi-characteristic and prove its invariance under cut-and-past operation. Our approach is analytic and follow very closely the method introduced by W. Zhang