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Conjugation spaces. (English) Zbl 1081.55006

This paper defines the notion of conjugation space and studies the properties of such spaces. These are spaces \(X\) having an involution \(T\) for which \(X\) and the fixed point set \(F\) of \(T\) have isomorphic mod 2 cohomology with dimensions doubled. The classic example is a complex Grassmannian with involution given by complex conjugation for which the fixed point set is a real Grassmannian. Many examples of conjugation spaces are exhibited.

MSC:

55N91 Equivariant homology and cohomology in algebraic topology
55M35 Finite groups of transformations in algebraic topology (including Smith theory)
53D05 Symplectic manifolds (general theory)
57R22 Topology of vector bundles and fiber bundles
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