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Cohomology of fixed point sets and deformation of algebras

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Abstract

Under certain conditions the cohomology algebra (with appropriate coefficients) of the fixed point set of a G-space (G=Z/pZ=Zp, p prime or G=S1) can be considered a deformation - in a purely algebraic sense - of the cohomology algebra of the space itself. On one hand this gives restrictions on the isomorphism type of algebras that can occur as cohomology algebra of the fixed point set of G-spaces if the cohomology algebra of the space itself is given. On the other hand it leads to the definition of obstructions for the cohomology algebra of the fixed point set to be isomorphic (as an ungraded algebra) to the cohomology algebra of the space itself.

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Puppe, V. Cohomology of fixed point sets and deformation of algebras. Manuscripta Math 23, 343–354 (1978). https://doi.org/10.1007/BF01167693

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  • DOI: https://doi.org/10.1007/BF01167693

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