A slice genus lower bound from sl(n) Khovanov–Rozansky homology

By Andrew Lobb. 2007

56 citations recorded by the source corpus.

We show that a generic perturbation of the doubly-graded Khovanov–Rozansky knot homology gives rise to a lower-bound on the slice genus of a knot. We prove a theorem about obtainable presentations of surfaces embedded in 4-space, which we use to simplify significantly our algebraic computations.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5694292cba109e0c0f7e56662034d2e7a142687e

How researchers see this paper

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In Computational Theory and Mathematics

1. P. Kronheimer
2. T. Mrowka
3. David E. V. Rose
4. Paul Wedrich
5. Christopher Woodward
6. K. Wehrheim

In Geometry and Topology

1. T. Mrowka
2. P. Kronheimer
3. David E. V. Rose
4. Paul Wedrich
5. M. Hedden
6. Christopher Scaduto
7. Peter S. Ozsv'ath
8. Christopher Herald

In Mathematical Physics

1. T. Mrowka
2. P. Kronheimer
3. Paul Wedrich
4. David E. V. Rose
5. M. Hedden
6. Christopher Scaduto
7. Ciprian Manolescu
8. Lenhard L. Ng

Citations in the corpus

• Deformations of colored sl(N) link homologies via foams (2015, methodology): “Lobb [28; 29] has used Gornik’s generic deformation of slN link homology to define concordance invariants that are analogous to Rasmussen’s invariant.”
• Knot homology groups from instantons (2008, methodology): “We make the following definition, modelled on similar constructions in [36, 32, 27].”