The C2-equivariant cohomology of complex projective spaces
Copyright policy )The C2-equivariant cohomology of complex projective spaces
We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside ring Mackey functor. This extension of the $RO(C_2)$-graded theory allows for the definition of Euler classes, which are used as generators of the cohomology of the projective spaces. As an application, we give an equivariant version of Bezout's theorem.
57 pages, this is a major update. The proof of the main result has been simplified. As an application an equivariant version of Bezout's theorem was added
Equivariant homology and cohomology in algebraic topology, Classical problems, Schubert calculus, projective space, equivariant characteristic class, Equivariant fiber spaces and bundles in algebraic topology, equivariant cohomology, Enumerative problems (combinatorial problems) in algebraic geometry, Homology of classifying spaces and characteristic classes in algebraic topology, Bézout's theorem, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 55N91 (Primary) 14N10, 14N15, 55R40, 55R91 (Secondary)
Equivariant homology and cohomology in algebraic topology, Classical problems, Schubert calculus, projective space, equivariant characteristic class, Equivariant fiber spaces and bundles in algebraic topology, equivariant cohomology, Enumerative problems (combinatorial problems) in algebraic geometry, Homology of classifying spaces and characteristic classes in algebraic topology, Bézout's theorem, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 55N91 (Primary) 14N10, 14N15, 55R40, 55R91 (Secondary)
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