Concordance of $Z_p\times\Z_p$ actions on $S^4$

Details Concordance of $Z_p\times\Z_p$ actions on $S^4$ Concordance of $Z_p\times\Z_p$ actions on $S^4$

2005-11-08

arxiv.org/abs/math/0511212v1

Algebraic & Geometric Topology 7, 2007, 785--796

Mathematics

Geometric Topology

Scientific paper

We consider locally linear Z_p x Z_p actions on the four-sphere. We present simple constructions of interesting examples, and then prove that a given action is concordant to its linear model if and only if a single surgery obstruction taking to form of an Arf invariant vanishes. We discuss the behavior of this invariant under various connected-sum operations, and conclude with a brief discussion of the existence of actions which are not concordant to their linear models.

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