Invariants of 4–manifolds from Khovanov–Rozansky link homology

Morrison, Scott¹ ; Walker, Kevin² ; Wedrich, Paul³

¹ Lyneham ACT, Australia
² Microsoft Station Q, Santa Barbara, CA, United States
³ Mathematical Sciences Institute, The Australian National University, Canberra ACT, Australia

Geometry & topology, Tome 26 (2022) no. 8, pp. 3367-3420.

Résumé

We use Khovanov–Rozansky ${\mathfrak{𝔤}\mathfrak{𝔩}}_N$ 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.

Détail

Keywords: TQFT, link homology, Khovanov homology, 4-manifolds, blob homology

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