Geometry and Topology Seminar

I compute the knot Floer complex for the regular fiber of \Sigma(2,3,7), and I show that its Seifert genus and genus in a self homology cobordism agree. The key step in this result was providing upgrades to the surgery formula for knot lattice homotopy. Ozsv\'ath, Stipsicz, and Szab\'o showed that knot lattice homology satisfies a surgery formula similar to the one relating knot Floer homology and Heegaard Floer homology. I provide an iterable version of this formula that given the doubly filtered knot lattice space with involutive maps for a generalized algebraic knot produces the corresponding data for the dual knot post-surgery.