Conjugations on 6-manifolds with free integral cohomology

TL;DR

This paper demonstrates the existence of conjugations on many simply-connected spin 6-manifolds with free integral cohomology, linking their cohomological properties to fixed point set conditions.

Contribution

It establishes conditions under which conjugations exist on 6-manifolds, especially highlighting the role of a degree-halving ring isomorphism in certain classes.

Findings

Conjugations exist on many simply-connected spin 6-manifolds.

The key condition is a degree-halving ring isomorphism between cohomologies.

The fixed point set is a 3-manifold M^3.

Abstract

In this article, we show the existence of conjugations on many simply-connected spin 6-manifolds with free integral cohomology. In a certain class the only condition on X^6 to admit a conjugation with fixed point set M^3 is the obvious one: the existence of a degree-halving ring isomorphism between the Z_2-cohomologies of X and M.