Return to Colloquia & Seminar listing

### Some geometric applications of the link Floer homology

**Geometry/Topology**

Speaker: | Beibei Liu, UC Davis |

Related Webpage: | https://www.math.ucdavis.edu/~bxliu/ |

Location: | 2112 MSB |

Start time: | Tue, Mar 12 2019, 1:30PM |

For links in the three sphere, there are two geometric questions: determining the Thurston polytope and 4-genus of links with vanishing pairwise linking numbers. I will explain how to use the Heegaard Floer homology introduced by Ozsvath and Szabo to determine the Thurston polytope, and give some bounds on the 4-genus in terms of the so-called h-function. In particular, for L-space links, the h-function can be computed explicitly by Alexander polynomials of the links and sublinks, and for L-space links with two components, the Thurston polytope is determined by the Alexander polynomials in a combinatorial way. I will also show some examples for both of the questions.