The RO(C₂)-graded cohomology of C₂-surfaces in\n underline\ℤ/2-coefficients

2019/07/16 by Christy Hazel, Hazel, Christy
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1907.07280

openalex publication_date 2019/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A surface with an involution can be viewed as a C₂-space where C₂ is\nthe cyclic group of order two. Using the classification of C₂-surfaces given\nby Dugger, we compute the RO(C₂)-graded Bredon cohomology of all\nC₂-surfaces in constant \ℤ/2 coefficients as modules over the\ncohomology of a point. We show the cohomology depends only on three numerical\ninvariants in the nonfree case, and only on two numerical invariants in the\nfree case.\n

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