Seminar Event Detail


Date:  Thursday, December 02, 2021
Location:  Virtual (3:00 PM to 4:00 PM)

Title:  On Murasugi sum and knot Floer homology

Abstract:   The Murasugi sum operation in knot theory provides an interesting generalization of the better-known connected sum operation. Gabai's work on taut foliations and sutured manifolds showed that the Murasugi sum interacts predictably with regard to geometric features of the knot pertaining to Seifert surfaces e.g. whether they are fibered, or minimal genus. Floer homology has provided algebraic invariants that can serve as receptors for some of the information provided by Gabai's techniques. In the context of Murasugi sums, Ni proved that the rank of a particular (extremal) knot Floer homology group is multiplicative under these operations. We refine Ni's result to show that Murasugi sums induce a graded tensor product of the extremal knot Floer homology groups and, moreover, that in certain cases one can obtain information about other invariants derived from knot Floer homology (so-called "tau" invariants). I'll give an overview of the Murasugi sum and some of its roles in low-dimensional topology, discuss our results, and their corresponding applications. This is joint work with Zhechi Cheng and Sucharit Sarkar.

Zoom link:


Speaker:  Matthew Hedden
Institution:  Michigan State University

Event Organizer:   Linh Truong   


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