Odd-dimensional Charney-Davis conjecture

TL;DR

This paper clarifies that the Charney-Davis Conjecture applies to both odd- and even-dimensional spheres, challenging the common perception that it is only relevant for odd dimensions.

Contribution

It demonstrates that the Charney-Davis Conjecture is valid for even-dimensional spheres, expanding its scope beyond traditional assumptions.

Findings

The conjecture applies to even-dimensional spheres.

The paper clarifies misconceptions about the conjecture's domain.

It provides a new perspective on the conjecture's applicability.

Abstract

More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres.