Topology Atlas | Conferences

Knots in the Triangle (Knots kNot in Washington)
April 29 - May 1, 2016
North Carolina State University
Raleigh NC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Independence of Whitehead Doubles of Torus Knots in the Smooth Concordance Group
by
Juanita Pinzon Caicedo
The University of Georgia

In the 1980’s Furuta and Fintushel-Stern applied the theory of instantons and Chern-Simons invariants to develop a criterion for a collection of special homology spheres to be independent in the homology cobordism group of oriented homology 3-spheres. Hedden and Kirk then used the aforementioned criterion to establish conditions under which an infinite family of Whitehead doubles of positive torus knots are independent in the smooth concordance group.

In the talk, I will review some of the definitions and constructions involved in the proof by Hedden and Kirk and I will introduce some topological constructions that simplify and extend their argument.

Date received: February 10, 2016

Copyright © 2016 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 # cbmk-02.