Month: August 2020

Triple linking and Heegaard Floer homology

| chrisman.76

Allison Moore (Virginia Commonwealth University)

We will describe several appearances of Milnor’s link invariants in the link Floer complex. This will include a formula that expresses the Milnor triple linking number in terms of the h-function. We will also show that the triple linking number is involved in a structural property of the d-invariants of surgery on certain algebraically split links. We will apply the above properties toward new detection results for the Borromean and Whitehead links. This is joint work with Gorsky, Lidman and Liu.

 

The Jones-Krushkal polynomial and minimal diagrams of surface links

| chrisman.76

Homayun Karimi (McMaster University)

We prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating
links in thickened surfaces. It implies that any reduced alternating diagram of a link
in a thickened surface has minimal crossing number, and any two reduced alternating
diagrams of the same link have the same writhe. This result is proved more generally
for link diagrams that are adequate, and the proof involves a two-variable generalization
of the Jones polynomial for surface links defined by Krushkal. The main result is
used to establish the first and second Tait conjectures for links in thickened surfaces
and for virtual links.  This is joint work with Hans Boden.