Knot Floer homology, link Floer homology and link detection

Binns, Fraser; Martin, Gage

doi:10.2140/agt.2024.24.159

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Knot Floer homology, link Floer homology and link detection

Fraser Binns and Gage Martin

Algebraic & Geometric Topology 24 (2024) 159–181

DOI: 10.2140/agt.2024.24.159

Abstract

We give new link detection results for knot and link Floer homology, inspired by recent work on Khovanov homology. We show that knot Floer homology detects $T (2, 4)$ , $T (2, 6)$ , $T (3, 3)$ , $L 7 n 1$ and the link $T (2, 2 n)$ with the orientation of one component reversed. We show link Floer homology detects $T (2, 2 n)$ and $T (n, n)$ , for all $n$ . Additionally, we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology.

Keywords

knot Floer homology, annular Khovanov homology, link detection

Mathematical Subject Classification

Primary: 57K10, 57K18

References

Publication

Received: 13 March 2021

Revised: 10 August 2022

Accepted: 26 August 2022

Published: 18 March 2024

Authors

Fraser Binns
Mathematics department Boston College Chestnut Hill, MA United States

Gage Martin
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 1 (2024)