Four Manifolds and two complexes with finite fundamental group

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• Johnny Nicholson (UCL)
• Friday 01 March 2019, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Nils Prigge.

In this talk, we will give an overview of various approaches to the classification of non-simply connected 4-manifolds using techniques from high-dimensional topology and the algebra of group rings. One approach is using a modified version of surgery theory, due to Kreck, to classify manifolds ‘stably’ up to connected sum with S2 x S2. This leaves us with the ‘unstable’ problem of cancelling the (S2 x S2)-summands, which we relate to the corresponding cancellation problems for 2-complexes up to wedging with S2 and Z[pi_1]-modules up to direct sum with a free module. We will report on recent progress on these cancellation problems, and on a related conjecture of C. T. C. Wall from the 1960s.

This talk is part of the Junior Geometry Seminar series.

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