Authors
Marko Stošić
Publication date
2007/3/29
Journal
Algebraic & Geometric Topology
Volume
7
Issue
1
Pages
261-284
Publisher
Mathematical Sciences Publishers
Description
In this paper we show that the nonalternating torus knots are homologically thick, ie that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot without changing certain part of its homology, and consequently, there exists stable homology of torus knots conjectured by Dunfield, Gukov and Rasmussen in [Experiment. Math. 15 (2006) 129–159]. Since our main tool is the long exact sequence in homology, we have applied our approach in the case of the Khovanov–Rozansky s l (n) homology, and thus obtained analogous stability properties of s l (n) homology of torus knots, also conjectured by Dunfield, Gukov and Rasmussen.
Total citations
Scholar articles
M Stošić - Algebraic & Geometric Topology, 2007
M Stošic - arXiv preprint math.GT/0511532