Conjugations on 6-manifolds with free integral cohomology
Martin Olbermann (MPIM Bonn)

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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
