Additivity for parametrized topological Euler characteristic and Reidemeister torsion

TL;DR

This paper demonstrates that recently defined parametrized topological Euler characteristic and Reidemeister torsion invariants satisfy additivity properties similar to their classical counterparts, enhancing understanding of bundle invariants.

Contribution

It establishes additivity formulas for parametrized topological Euler characteristic and Reidemeister torsion, extending classical invariants to bundle settings.

Findings

Additivity formulas for parametrized invariants

Extension of classical invariants to bundle context

Enhanced understanding of bundle invariants

Abstract

Dwyer, Weiss, and Williams have recently defined the notions of parametrized topological Euler characteristic and parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and Reidemeister torsion of finite CW-complexes.