Virtual Covers of Links II
Micah Chrisman, Aaron Kaestner

TL;DR
This paper introduces semi-fibered concordance for links with a fibered component, using virtual covers to define invariants that obstruct certain slice and ribbon discs, and explores applications to satellite operators and knots in fibered 3-manifolds.
Contribution
It develops the concept of semi-fibered concordance for links, utilizing virtual covers to produce new invariants and applications in knot theory.
Findings
The virtual knot associated to a link is a semi-fibered concordance invariant.
Obstructions to slice and ribbon discs are derived from these invariants.
Applications include results on satellite operators and knots in fibered 3-manifolds.
Abstract
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 with 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 where is "close to" a fiber of . Such are studied with virtual covers, where a virtual knot is associated to . We show that the concordance class of is a semi-fibered concordance invariant. This gives obstructions for certain slice and ribbon discs for the component. Further applications are to injectivity of satellite operators in semi-fibered concordance and to knots in fibered -manifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology
