Twisted Higher Smooth Torsion

TL;DR

This paper extends the concept of cohomological higher smooth torsion to include twisting, demonstrating that it maintains key properties like additivity and transfer, which are crucial for geometric and coefficient-based applications.

Contribution

It introduces a twisted version of cohomological higher smooth torsion, preserving essential properties such as additivity and transfer.

Findings

The twisted higher smooth torsion satisfies geometric additivity.

It also satisfies transfer properties for coefficients.

The extension maintains core invariance properties.

Abstract

In this paper we extend Badzioch's, Dorabiala's, and Williams' definition of cohomological higher smooth torsion to a twisted cohomological higher torsion invariant. Additionally, we show that this still satisfies geometric additivity and transfer, and will also satisfy additivity and transfer for coefficients.