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2007 Homological thickness and stability of torus knots
Marko Stošić
Algebr. Geom. Topol. 7(1): 261-284 (2007). DOI: 10.2140/agt.2007.7.261

Abstract

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 sl(n) homology, and thus obtained analogous stability properties of sl(n) homology of torus knots, also conjectured by Dunfield, Gukov and Rasmussen.

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Marko Stošić. "Homological thickness and stability of torus knots." Algebr. Geom. Topol. 7 (1) 261 - 284, 2007. https://doi.org/10.2140/agt.2007.7.261

Information

Received: 24 September 2006; Accepted: 22 November 2006; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1156.57010
MathSciNet: MR2308944
Digital Object Identifier: 10.2140/agt.2007.7.261

Subjects:
Primary: 57M25

Rights: Copyright © 2007 Mathematical Sciences Publishers

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