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Transactions of the American Mathematical Society

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On the rational homotopy Lie algebra of a fixed point set of a torus action


Authors: Christopher Allday and Volker Puppe
Journal: Trans. Amer. Math. Soc. 297 (1986), 521-528
MSC: Primary 57S99; Secondary 55P62, 55Q91
DOI: https://doi.org/10.1090/S0002-9947-1986-0854082-0
MathSciNet review: 854082
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Abstract: Let $ X$ be a simply connected topological space, and let $ {\mathcal{L}_{\ast}}(X)$ be its rational homotopy Lie algebra. Suppose that a torus acts on $ X$ with fixed points, and suppose that $ F$ is a simply connected component of the fixed point set. If $ {\mathcal{L}_{\ast}}(X)$ is finitely presented and if $ F$ is full, then it is shown that $ {\mathcal{L}_{\ast}}(F)$ is finitely presented, and that the numbers of generators and relations in a minimal presentation of $ {\mathcal{L}_{\ast}}(F)$ do not exceed the numbers of generators and relations (respectively) in a minimal presentation of $ {\mathcal{L}_{\ast}}(X)$. Various other related results are given.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0854082-0
Keywords: Torus actions, rational homotopy Lie algebra, generators and relations, cup length
Article copyright: © Copyright 1986 American Mathematical Society