No Access

KNOT HOMOLOGY OF (3, m) TORUS KNOTS

WILLIAM D. GILLAM

Department of Mathematics, Columbia University, New York, NY 10027, USA

https://doi.org/10.1142/S0218216512500721Cited by:1 (Source: Crossref)

Abstract

We give a direct computation of the Khovanov knot homology of the (3, m) torus knots/links. Our computation yields complete results with ℤ[½] coefficients, though we leave a slight ambiguity concerning 2-torsion when integer coefficients are used. Our computation uses only the basic long exact sequence in knot homology and Rasmussen's result on the triviality of the embedded surface invariant.

Keywords:

AMSC: 57M25, 57M27

References

D. Bar-Natan, Geom. Topol. 9, 1443 (2005). Crossref, Web of Science, Google Scholar
M. Jacobsson, Algebr. Geom. Top. 4, 1211 (2004). Crossref, Google Scholar
M. Khovanov, Duke Math. J. 101, 359 (2000). Crossref, Web of Science, Google Scholar
M. Khovanov, An invariant of tangle cobordisms, to appear in Trans. Amer. Math. Soc . Google Scholar
E.-S. Lee, Adv. Math. 197(2), 554 (2005). Crossref, Web of Science, Google Scholar
J. Rasmussen, Khovanov homology and the slice genus, preprint (2004) , arXiv:math.GT/0402131 . Google Scholar
J. Rasmussen, Khovanov's invariant for closed surfaces, preprint (2004) , arXiv:math/0405474 . Google Scholar
M. Stosic, Homology of torus links, preprint (2006) , arXiv:math/0606656 . Google Scholar
P. Turner, A spectral sequence for Khovanov homology with an application to (3, q)- torus links, preprint (2006) , arXiv:math.GT/0606369 . Google Scholar