On the invariance of the Dowlin spectral sequence

Tripp, Samuel; Winkeler, Zachary

doi:10.2140/agt.2024.24.5123

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On the invariance of the Dowlin spectral sequence

Samuel Tripp and Zachary Winkeler

Algebraic & Geometric Topology 24 (2024) 5123–5159

DOI: 10.2140/agt.2024.24.5123

Abstract

Given a link $L$ , Dowlin constructed a filtered complex inducing a spectral sequence with $E_{2}$ –page isomorphic to the Khovanov homology $\bar{Kh} (L)$ and $E_{\infty}$ –page isomorphic to the knot Floer homology $\hat{H F K} (m (L))$ of the mirror of the link. We prove that the $E_{k}$ –page of this spectral sequence is also a link invariant, for $k \geq 3$ .

Keywords

Khovanov homology, knot Floer homology, knot theory, spectral sequence, invariants

Mathematical Subject Classification

Primary: 57K18

References

Publication

Received: 29 January 2023

Revised: 8 August 2023

Accepted: 8 October 2023

Published: 27 December 2024

Authors

Samuel Tripp
Department of Mathematical Sciences Worcester Polytechnic Institute Worcester, MA United States
http://samueltripp.github.io
Zachary Winkeler
Clark Science Center Smith College Northampton, MA United States
http://zach-winkeler.github.io

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Volume 24, issue 9 (2024)