Constructions of exotic actions on product manifolds with an asymmetric factor
| Autor: | Błaszczyk, Zbigniew, Kaluba, Marek |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We explore transformation groups of manifolds of the form $M\times S^n$, where $M$ is an asymmetric manifold, i.e. a manifold which does not admit any non-trivial action of a finite group. In particular, we prove that for $n=2$ there exists an infinite family of distinct non-diagonal effective circle actions on such products. A similar result holds for actions of cyclic groups of prime order. We also discuss free circle actions on $M \times S^1$, where $M$ belongs to the class of "almost asymmetric" manifolds considered previously by V. Puppe and M. Kreck. Comment: Theorem 4 has been renamed to Proposition 4; it now has an additional assumption and a new proof. Numerous minor improvements throughout the text to improve readability. 10 pages, no figures |
| Databáze: | arXiv |
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