Constructions of exotic actions on product manifolds with an asymmetric factor

2016/03/15 by Zbigniew Błaszczyk, Błaszczyk, Zbigniew, Marek Kaluba +1
Mathematics · #57S25 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1603.04888

openalex publication_date 2016/03/15 · openalex created_date 2022/10/10 · openalex updated_date 2026/07/28

Abstract

We explore transformation groups of manifolds of the form M× Sⁿ, 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 × S¹, where M belongs to the class of "almost asymmetric" manifolds considered previously by V. Puppe and M. Kreck.

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