Seminar

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Smith theory is primarily concerned with actions of finite groups on familiar spaces such as finite dimensional CW complexes and manifolds. The theory relates the cohomology of a space with a finite group action to the cohomology of the subspace of its fixed points. One of such relationships between their cohomologies is given by the Smith inequality in classical topology which gives some algebraic and topological information about some spaces. Then this inequality appeared in many different settings such as low dimensional topology, various Floer cohomologies, and Hochschild homology. In this talk, I will show a Smith-type inequality in the fixed point Floer cohomology, which is an invariant introduced by Andreas Floer which associates to a symplectic manifold M and a symplectic automorphism of M a Z/2 graded Z/2 - vector space. This inequality is due to Kristen Hendricks.