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.