3/30/2006
Elisenda Grigsby,
UC Berkeley
Knot Floer Homology for Cyclic Branched Covers
Knot Floer homology, introduced by Ozsvath and Szabo and independently
by Rasmussen, associates a sequence of graded abelian groups to a
nullhomologous knot in a closed three-manifold.
In my talk, I will discuss the knot Floer homology of the preimage of a knot inside its cyclic branched covers, focusing particular attention on the double-branched covers of two-bridge knots in S3. In this setting, the invariants are not much more difficult to compute than the knot Floer homology of the original knot in S3. Furthermore, they contain strictly
more information and, hence, should yield enhanced data about the knot.