Work

Characterizing maximal varieties via Bredon cohomology

Year: 2025

Type: article

Abstract: We obtain a characterization of Maximal and Galois-Maximal C 2 -spaces (including real algebraic varieties) in terms of RO ( C 2 ) -graded cohomology with coefficients in the constant Mackey functor F _ 2 , using the structure theorem of Clover May. Other known characterizations, for instance in terms of equivariant Borel cohomology, are also rederived from this. For the particular case of a smooth projective real variety V , equivariant Poincaré duality is used to deduce further symmetry restrictions for the decomposition of the RO ( C 2 ) -graded cohomology of the complex locus V ( C ) given by the same structure theorem. We illustrate this result with some computations, including the RO ( C 2 ) -graded cohomology with F _ 2 coefficients of real K 3 surfaces.

Source: Topology and its Applications

DOI: 10.1016/j.topol.2025.109544

Authors: Pedro F. dos Santos, Carlos Florentino, Javier Orts

Institutions: Instituto Superior Técnico, University of Lisbon

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,920

Funders: Fundação para a Ciência e a Tecnologia, Instituto Superior Técnico