On the rational homotopy Lie algebra of a fixed point set of a torus action
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- by Christopher Allday and Volker Puppe PDF
- Trans. Amer. Math. Soc. 297 (1986), 521-528 Request permission
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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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