2015/12/08 by Micah Chrisman, Chrisman, Micah, Aaron Kaestner +1
Mathematics · #Geometric and Algebraic Topology #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1512.02667
A fibered concordance of knots, introduced by Harer, is a concordance between fibered knots that is well-behaved with respect to the fibrations. We consider semi-fibered concordance of two component ordered links L=J \sqcup K with J fibered. These are concordances that restrict to fibered concordances on the first component. Motivated by some examples of Gompf-Scharlemann-Thompson, we further limit our attention to those links L where K is "close to" a fiber of J. Such L are studied with virtual covers, where a virtual knot υ is associated to L. We show that the concordance class of υ is a semi-fibered concordance invariant. This gives obstructions for certain slice and ribbon discs for the K component. Further applications are to injectivity of satellite operators in semi-fibered concordance and to knots in fibered 3-manifolds.