Stanford University

Smoothing finite group actions on three-manifolds

Bldg 380 Room 380C
Friday, January 11, 2019 4:00 PM
John Pardon (Harvard University)

Abstract: There exist continuous finite group actions on three-manifolds which are not smoothable, in the sense that they are not smooth with respect to any smooth structure.  For example, Bing constructed an involution of the three-sphere whose fixed set is a wildly embedded two-sphere.  However, one can still ask whether every continuous finite group action on a three-manifold can be uniformly approximated by a smooth action.  We outline an approach to answering this question in the affirmative, based on the author's work on the Hilbert--Smith conjecture in dimension three.