Rational tangle replacements and knot Floer homology
Location
Among early applications of gauge theory invariants in knot theory, the proof of Milnor conjecture on the unknotting number of the torus knots by Kronheimer and Mrowka is an amazing highlight. Later, several lower bounds for the unknotting number were constructed from knot Floer homology and Khovanov homology, in form of homomorphisms from the concordance group of knots to the integers (or other abelian groups). Lower bounds for the unknotting number which are not concordance invariants were introduced in the past 5 years. Nevertheless, it is recently shown by Iltgen, Lewark and Marino that all the lower bounds from Khovanov homology are in fact lower bounds for the proper rational distance. In this talk, we will have a look at the parallel story in knot Floer theory. In particular, we construct lower bounds for the rational distance and proper rational distance from knot Floer homology.
Note that this talk is later than usual.