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Invariants of $4$–manifolds from Khovanov–Rozansky link homology

Scott Morrison, Kevin Walker and Paul Wedrich

Geometry & Topology 26 (2022) 3367–3420
DOI: 10.2140/gt.2022.26.3367
Abstract

We use Khovanov–Rozansky 𝔤𝔩N link homology to define invariants of oriented smooth 4–manifolds, as skein modules constructed from certain 4–categories with well-behaved duals.

The technical heart of this construction is a proof of the sweep-around property, which makes these link homologies well defined in the 3–sphere.

Keywords
TQFT, link homology, Khovanov homology, 4-manifolds, blob homology
Mathematical Subject Classification
Primary: 57K18, 57R56
References
Publication
Received: 9 June 2020
Revised: 17 May 2021
Accepted: 26 June 2021
Published: 16 March 2023
Proposed: Ciprian Manolescu
Seconded: Stavros Garoufalidis, David Gabai
Authors
Scott Morrison
Lyneham ACT
Australia
https://tqft.net
Kevin Walker
Microsoft Station Q
Santa Barbara, CA
United States
http://canyon23.net/math/
Paul Wedrich
Mathematical Sciences Institute
The Australian National University
Canberra ACT
Australia
http://paul.wedrich.at