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Surfaces in 4-manifolds and 1-stable equivalence

Banff International Research Station for Mathematical Innovation and Discovery

The Wall's stable h-cobordism theorem states that homotopy equivalent, smooth simply-connected 4-manifolds become diffeomorphic after stabilizing, i.e. connected summing with some finite number of a S^2-bundle over S^2. And, in fact, all known examples need only one stabilization to be diffeomorphic. In this talk, we will talk about the analogous stabilization question for knotted surfaces in simply-connected 4-manifolds produced by all of the known constructions based on Fintushel-Stern knot surgery. And we will prove that any pair of these knotted surfaces that preserve the fundamental groups of their complements become all diffeomorphic after single stabilization.

Mathematics; Manifolds and cell complexes; Global analysis, analysis on manifolds; Low dimensional topology

video/mp4

Author affiliation: Seoul National University

2018-02-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64583

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/