Invariants of 4-manifolds from Khovanov-Rozansky link homology
Scott Morrison, Kevin Walker, Paul Wedrich
TL;DR
This paper introduces new invariants for oriented smooth 4-manifolds derived from Khovanov-Rozansky link homology, utilizing skein modules and 4-categories, with a key proof of the sweep-around property ensuring well-definedness.
Contribution
It develops a novel approach to 4-manifold invariants using link homology and categorical techniques, establishing foundational properties for these invariants.
Findings
Defined invariants of 4-manifolds from link homology
Proved the sweep-around property for well-definedness
Constructed skein modules from 4-categories
Abstract
We use Khovanov-Rozansky gl(N) 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.
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