A computation in Khovanov-Rozansky Homology
Daniel Krasner
TL;DR
This paper explores the computation of Khovanov-Rozansky homology for tangles, revealing simplifications and proposing a local algorithm, with comparisons to foam-based sl_3-homology methods.
Contribution
It introduces a local algorithm for computing Khovanov-Rozansky homology and demonstrates simplifications in the complexes involved.
Findings
Complexes reduce to very simple forms
A local computation algorithm is proposed
Results are compared with foam-based sl_3-homology
Abstract
We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl_3-homology.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology