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1-stable equivalence of knotted surfaces in 4-manifolds
by
Hee Jung Kim
Seoul National University
Coauthors: Dave Auckly (Kansas State University), Paul Melvin (Bryn Mawr College), Daniel Ruberman (Brandeis University), Hannah Schwartz (Bryn Mawr College)
In 4-dimensional topology, the existence of exotic smooth structures on closed simply-connected 4-manifolds derives from work of Donaldson and Freedman, and it is known by Wall that such manifolds become diffeomorphic after stabilizing, i.e. connected summing with a S^2-bundle over S^2, sufficiently many times. The question of the minimal number of stabilizations to be diffeomorphic arises and it has turned out that a single stabilization suffices for all known examples.
In this talk, we will discuss an analogue of this principle related to embedded surfaces in 4-manifolds. In particular, we will show that the 1-stable equivalence principle holds for surfaces with simply-connected complements; any two homologous surfaces of the same genus embedded in a smooth 4-manifold with simply-connected complements are smoothly isotopic after 'single' stabilization with a S^2-bundle over S^2.
Date received: November 20, 2017
Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cboj-13.