The C₂-equivariant ordinary cohomology of complex quadrics II: The symmetric case

2025/11/18 by Costenoble, Steven R., Hudson, Thomas
Mathematics · #14N15 #55N25 #55N91 (Primary) #57R91 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.14251

openalex publication_date 2025/11/18 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/28

Abstract

In this, the second of three papers about C₂-equivariant complex quadrics, we calculate the equivariant ordinary cohomology of smooth symmetric quadrics graded on the representation ring of ΠBU(1) and with coefficients in the Burnside Mackey functor. These calculations exhibit various interesting properties, including the first naturally occurring example we are aware of where the cohomology is not just the sum of shifted copies of the cohomology of a point, but also has summands that are shifted copies of the cohomology of the free orbit C₂/e.

Citations

• The C₂-equivariant ordinary cohomology of complex quadrics III: Exceptional cases
• A geometric C₂-equivariant Bézout Theorem
• A Freeness Theorem for RO(Z/2)-graded Cohomology
• Characteristic classes and quadric bundles

Related

• The C₂-equivariant ordinary cohomology of complex quadrics III: Exceptional cases
• The C₂-equivariant ordinary cohomology of complex quadrics I: The antisymmetric case
• The C₂-equivariant ordinary cohomology of BU(2)
• The C₂-equivariant ordinary cohomology of BT²
• Bigraded Equivariant Cohomology of Real Quadrics