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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References
BREDON, G.E.: Introduction to Compact Transformation Groups. New York-London: Academic Press 1972
CHANG, T.: On the number of relations in the cohomology of a fixed point set. Manuscripta math. 18, 237–247 (1976)
GABRIEL, P.: Finite representation type is open. Springer, Lecture Notes in Math. Vol.488, 132–155 (1975)
GERSTENHABER, M.: On the deformation of rings and algebras. Ann. of Math. 79, 59–103 (1964)
GERSTENHABER, M.: On the deformation of rings and algebras IV. Ann. of Math. 99, 257–276 (1974)
HSIANG, W.Y.: Cohomology Theory of Topological Transformation Groups. Berlin-Heidelberg-New York: Springer 1975
MASSEY, W.S. and PETERSON, F.P.: The cohomology structure of certain fibre spaces-I, Topology 4, 47–65 (1965)
PUPPE, V.: On a conjecture of Bredon. Manuscripta math. 12, 11–16 (1974)
ANDRE, M.: Homologie des algèbres commutatives. Berlin-Heidelberg-New York: Springer 1974
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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