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On some $p$–differential graded link homologies, II

You Qi and Joshua Sussan

Algebraic & Geometric Topology 23 (2023) 3357–3394
Abstract

In a previous article, we constructed a link invariant categorifying the Jones polynomial at a 2p th root of unity, where p is an odd prime. This categorification utilized an N = 2 specialization of a differential introduced by Cautis in an 𝔰𝔩N–link homology theory. Here we give a family of link homologies where the Cautis differential is specialized to a positive integer of the form N = kp + 2. When k is even, all these link homologies categorify the Jones polynomial evaluated at a 2p th root of unity, but they are distinct link invariants.

Keywords
categorification, hopfological algebra, link homology, Jones polynomial, prime root of unity
Mathematical Subject Classification
Primary: 57K18
Secondary: 18G99
References
Publication
Received: 11 December 2021
Revised: 1 April 2022
Accepted: 21 April 2022
Published: 26 September 2023
Authors
You Qi
Department of Mathematics
University of Virginia
Charlottesville, VA
United States
Joshua Sussan
Department of Mathematics
CUNY Medgar Evers
Brooklyn, NY
United States
Mathematics Program
The Graduate Center, CUNY
New York, NY
United States

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