
Organizers 
Stable Concordance Genus of Knots
by
Kate Kearney
Louisiana State University
The concordance genus of a knot is the least threegenus of a knot concordant to the knot. The concordance genus is bounded below by the fourgenus (or slice genus), and bounded above by the threegenus. This makes the concordance genus a valuable tool to describe the difference between these invariants. In simple cases the concordance genus is not difficult to calculate, since there are a variety of algebraic tools that give bounds for the concordance genus. Unfortunately, as the crossing number increases, it becomes increasingly difficult to find concordances. The stable concordance genus, which we will discuss in this talk, describes the behavior of the concordance genus of a given knot under connect sum. We will briefly define the invariant, give some examples of calculations, and discuss applications to the study of concordance.
Date received: December 11, 2013
Copyright © 2013 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 # cbid11.