Removing double points of immersions

Mark Grant (University of Edinburgh)

Monday 23rd November, 2009 16:00-17:00 Mathematics Building, room 204


The following question is motivated by Surgery Theory: Given an immersion of the n-sphere into an m-manifold M, how can we tell if it is regularly homotopic to an embedding? This talk will survey results in this area, focussing on complete obstructions defined in terms of the fundamental group ring and higher homotopy groups of M. The case m=2n was done by Terry Wall in the 1960's, building on earlier work of Hassler Whitney. The case m=2n-1 and M is Euclidean space was done by Tobias Ekholm in 1998. We will discuss recent progress on the general case when M is a manifold of dimension 2n-1. This is an ongoing project with Andrew Ranicki in Edinburgh.

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