||Pseudo-meridians of knot groups
A pseudo-meridian of the group of a knot in the 3-sphere is an element that normally generates the group, but is not automorphic to a meridian. In this talk, we will see that many knot groups contain an infinite number of pseudo-meridians (up to automorphism), and that the existence of such elements is connected with Simon's conjecture (Problem 1.12 (D) of Rob Kirby's list) and with other questions concerning knot-group epimorphisms.
||Joshua Greene (Columbia)
||Conway mutation and alternating links
Let D and D' denote connected, reduced, alternating diagrams for a pair of links, and Y and Y' their branched double-covers. I'll discuss the proof and consequences of the following result: Y and Y' have isomorphic Heegaard Floer homology groups iff Y and Y' are homeomorphic iff D and D' are mutants.
||Jennifer Hom (U Penn)
||Concordance and the knot Floer complex
We will use the knot Floer complex, in particular the
invariant epsilon, to define a new smooth concordance homomorphism.
Applications include a formula for tau of iterated cables, better
bounds (in many cases) on the 4-ball genus than tau alone, and a new
infinite family of smoothly independent topologically slice knots. We
will also discuss various algebraic properties of this construction,
including a total ordering, a ``much greater than'' relation, and a