A link-splitting spectral sequence in Khovanov homology

By Joshua D. Batson, Cotton Seed. 2013

57 citations recorded by the source corpus.

We construct a new spectral sequence beginning at the Khovanov homology of a link and converging to the Khovanov homology of the disjoint union of its components. The page at which the sequence collapses gives a lower bound on the splitting number of the link, the minimum number of times its components must be passed through one another in order to completely separate them. In addition, we build on work of Kronheimer-Mrowka and Hedden-Ni to show that Khovanov homology detects the unlink.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b8b699acf790207372c952ef52dbaf5020556da5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Michael Ehrig
2. D. Tubbenhauer
3. Paul Wedrich

In Geometry and Topology

1. Michael Ehrig
2. D. Tubbenhauer
3. Paul Wedrich

In Mathematical Physics

1. Michael Ehrig
2. D. Tubbenhauer
3. Paul Wedrich

Citations in the corpus

• Functoriality of colored link homologies (2017, background): “Ni [HN13] have shown that they enable Khovanov homology to detect unlinks (it was later proven that the module structure is determined by the bigraded vector space structure in the case of the unlink [BS15]) , see also Wu [Wu17] for a related result for the triply-graded homology. Module structures ”