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Deformations of algebras and cohomology of fixed point sets

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Abstract

In [13] it is shown that under certain conditions the cohomology algebra of the fixed point set of a space with group action is in an algebraic sense a deformation of the cohomology algebra of the space itself. Here we attempt to prove a converse of the above statement, i.e. we try to realize geometrically a given algebraic deformation of a (commutative) graded algebras as the cohomology algebra of the fixed point set of a suitable space with group action. The first part of this note in a sense reduces this realization problem in equivariant topology to a non-equivariant problem while the second part uses Sullivan's theory of minimal models to actually obtain a converse for S1-actions, where cohomology is taken with rational coefficients.

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  1. Fachbereich Mathematik, Universität Konstanz, Universitätsstraße 10, 7750, Konstanz, Bundesrepublik Deutschland

    Volker Puppe

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  1. Volker Puppe
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Puppe, V. Deformations of algebras and cohomology of fixed point sets. Manuscripta Math 30, 119–136 (1979). https://doi.org/10.1007/BF01300965

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