Dear Topologists and Friends of Topology,

     We will have a seminar this Thursday (MSCS 514 at 3:30) given by Shelly Harvey, from Rice University.

Title: Metric Aspects of Knot Concordance

Abstract:  We are interested in the set of knot up to concordance, denoted C.   C is an abelian group but its structure is not very well understood.  We propose a new approach to understanding C, namely
considering C as a metric space on which there exists many natural operators.  Since one example of such an operator is connected-sum with a fixed knot, this approach is arguably more general than focusing on C as an abelian group. In fact, it was previously suggested by the authors along with C. Leidy that C is a fractal space and the proposed self-similarities of C are classical satellite operations.   Very recently, Cochran-Davis-Ray proved that many of these satellite operators (strong winding number 1) are indeed injective, modulo the smooth 4-dimensional Poincare Conjecture .  We show that that these operators are, in fact, isometric embeddings while winding number zero satellite operators are, by contrast, approximate contractions.  This is joint work with Tim Cochran.