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Bordered Heegaard Floer homology and the tau-invariant of cables
by
Jennifer Hom
University of Pennsylvania
We will use bordered Heegaard Floer homology to give a formula for the Ozsvath-Szabo concordance invariant tau of the (p, q)-cable of a knot K in terms of p, q, and two concordance invariants, tau(K) and epsilon(K), associated to the knot Floer complex of K. As a consequence, we will show that for any integer n, there exist knots K and K' with tau(K)=tau(K')=n such that tau of the (p, q)-cables of K and K' are not equal for any pair of relatively prime integers p and q. Finally, we will discuss some of the properties of epsilon; in particular, epsilon is strictly stronger than tau in determining obstructions to a knot being slice.
Date received: April 25, 2010
Copyright © 2010 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 # cbaf-10.