February 2, 2007

Swatee Naik (University of Nevada at Reno)

Title: Order in the Concordance Group

Abstract: Concordance classes of knots form an abelian group under connected sum. The smooth concordance group naturally maps onto the topological one with a non-trivial kernel. The topological concordance group, in turn, maps onto the algebraic concordance group of equivalence classes of Seifert forms, which is a direct sum of countably infinite copies of the infinite cyclic group and of finite cyclic groups of orders 2 and 4. Previously Casson-Gordon invariants have been used to show that certain order four Seifert forms cannot be represented by finite topological concordance order knots. Recently by Jabuka-Naik and by Grigsby-Ruberman-Strle, invariants from Heegaard-Floer homology have been used to improve on lower bounds on the smooth concordance order of small crossings knots. In this talk I will outline the work related to eliminating finite, topological as well as smooth concordance order of knots.