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The nontriviality of the first rational homology group of some connected invariant subsets of periodic transformations

Authors: Amir Assadi and Dan Burghelea
Journal: Proc. Amer. Math. Soc. 88 (1983), 701-707
MSC: Primary 57S17; Secondary 57S10
Erratum: Proc. Amer. Math. Soc. 94 (1985), 187.
MathSciNet review: 702303
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Abstract: This note was inspired by some results of P. A. Smith [S]. One proves that for any periodic map of a manifold $ M$ and any codimension two invariant submanifold $ P$ of $ M$ containing part of the stationary point set, connected invariant subsets of the complement of $ P$ must carry nontrivial one-dimensional rational cycles, provided that $ M$ satisfies some simple homological conditions (Theorem A). This fact has interesting consequences in transformation group theory.

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Article copyright: © Copyright 1983 American Mathematical Society