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Describing surfaces and isotopies in 4-manifolds via banded unlinks
by
Mark Hughes
Brigham Young University
Coauthors: Seungwon Kim and Maggie Miller
There are a number of well-established ways to represent knotted surfaces and isotopies between them in S^4, including motion pictures with movie moves, or broken surface diagrams with Roseman moves. In this talk I will discuss another method of representing surfaces in 4-space via banded unlink diagrams, which can also be used to describe surfaces in an arbitrary oriented 4-manifold X. I will present a set of moves which are sufficient to relate any two banded unlink presentations of isotopic surfaces in X, which generalizes a theorem in S^4 due to Swenton. Time permitting I will outline some applications of this approach to studying surfaces via banded unlinks.
Date received: December 10, 2018
Copyright © 2018 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 # cbpq-25.