Braiding link cobordisms and non-ribbon surfaces

作者：Hughes Mark C^*

来源：Algebraic and Geometric Topology, 2015, 15(6): 3707-3729.

DOI：10.2140/agt.2015.15.3707

We define the notion of a braided link cobordism in S-3 x [0, 1], which generalizes Viro's closed surface braids in R-4. We prove that any properly embedded oriented surface W subset of S-3 x [0, 1] is isotopic to a surface in this special position, and that the isotopy can be taken rel boundary when partial derivative W already consists of closed braids. These surfaces are closely related to another notion of surface braiding in D-2 x D-2, 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.

• 出版日期2015