Volume 15, issue 6 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Braiding link cobordisms and non-ribbon surfaces

Mark C Hughes

Algebraic & Geometric Topology 15 (2015) 3707–3729
Abstract

We define the notion of a braided link cobordism in S3 × [0,1], which generalizes Viro’s closed surface braids in 4. We prove that any properly embedded oriented surface W S3 × [0,1] is isotopic to a surface in this special position, and that the isotopy can be taken rel boundary when W already consists of closed braids. These surfaces are closely related to another notion of surface braiding in D2 × D2, called braided surfaces with caps, which are a generalization of Rudolph’s braided surfaces. We mention several applications of braided surfaces with caps, including using them to apply algebraic techniques from braid groups to studying surfaces in 4–space, as well as constructing singular fibrations on smooth 4–manifolds from a given handle decomposition.

Keywords
braids, links, knot cobordisms
Mathematical Subject Classification 2010
Primary: 57M12
Secondary: 57M25, 57R52
References
Publication
Received: 2 March 2015
Revised: 31 March 2015
Accepted: 12 April 2015
Published: 12 January 2016
Authors
Mark C Hughes
Department of Mathematics
Brigham Young University
312 TMCB
Provo, UT 84602
USA
http://math.byu.edu/~hughes/