Maximal Antipodal Sets and the Topology of Generalised Symmetric Spaces

TL;DR

This paper proves longstanding conjectures about the size of maximal antipodal sets in symmetric spaces, extending results to generalized symmetric spaces of finite abelian p-groups using equivariant cohomology techniques.

Contribution

It extends Chen--Nagano's conjectures to generalized symmetric spaces of finite abelian p-groups and verifies them using equivariant cohomology methods.

Findings

Confirmed conjectures for symmetric spaces.

Extended conjectures to generalized symmetric spaces.

Utilized equivariant cohomology techniques.

Abstract

We prove several long-standing conjectures by Chen--Nagano on cohomological descriptions of the cardinalities of maximal antipodal sets in symmetric spaces. We actually extend these conjectures to the setting of generalised symmetric spaces of finite abelian $p$-groups and verify them mostly in this broader context drawing upon techniques from equivariant cohomology theory.