Maximal Antipodal Sets and the Topology of Generalised Symmetric Spaces

2021/01/05 by Manuel Amann, Amann, Manuel · 1 citation
Mathematics · #53C35 (Primary) #55N25 (Secondary) #57N65 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2101.01587

openalex publication_date 2021/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Polars and antipodal sets of generalized s-manifolds

Related

• Maximal antipodal sets in irreducible compact symmetric spaces
• Antipodal sets of exceptional symmetric spaces
• A complete description of the antipodal set of most symmetric spaces of compact type
• Natural Γ-symmetric structures on R-spaces
• Polars and antipodal sets of generalized s-manifolds