Geodesic
Homological thickness and stability of torus knots
Stošić, Marko1
1Instituto de Sistemas e Robótica and CAMGSD, Instituto Superior Técnico, TU Lisbon, Av Rovisco Pais 1, 1049-001 Lisbon, Portugal
Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 261-284
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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.

DOI : 10.2140/agt.2007.7.261
Keywords: Khovanov homology, torus knots, thickness, stability

Stošić, Marko  1

1 Instituto de Sistemas e Robótica and CAMGSD, Instituto Superior Técnico, TU Lisbon, Av Rovisco Pais 1, 1049-001 Lisbon, Portugal 
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Stošić, Marko. Homological thickness and stability of torus knots. Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 261-284. doi: 10.2140/agt.2007.7.261

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