Maximal Antipodal Sets and the Topology of Generalised Symmetric Spaces

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.