Authors: | Stošić, Marko | Title: | Khovanov homology of torus links | Journal: | Topology and its Applications | Volume: | 156 | Issue: | 3 | First page: | 533 | Last page: | 541 | Issue Date: | 1-Jan-2009 | Rank: | M23 | ISSN: | 0166-8641 | DOI: | 10.1016/j.topol.2008.08.004 | Abstract: | In this paper we show that there is a cut-off in the Khovanov homology of (2 k, 2 k n)-torus links, namely that the maximal homological degree of non-zero homology groups of (2 k, 2 k n)-torus links is 2 k2 n. Furthermore, we calculate explicitly the homology group in homological degree 2 k2 n and prove that it coincides with the center of the ring Hk of crossingless matchings, introduced by M. Khovanov in [M. Khovanov, A functor-valued invariant for tangles, Algebr. Geom. Topol. 2 (2002) 665-741, arXiv:math.QA/0103190]. This gives the proof of part of a conjecture by M. Khovanov and L. Rozansky in [M. Khovanov, L. Rozansky, A homology theory for links in S2 × S1, in preparation]. Also we give an explicit formula for the ranks of the homology groups of (3, n)-torus knots for every n ∈ N. |
Keywords: | Hochschild cohomology | Khovanov homology | Torus knots | Publisher: | Elsevier | Project: | FEDER, project Quantum Topology POCI/MAT/60352/2004 Ministry of Science of Serbia, project 144032 |
Show full item record
SCOPUSTM
Citations
22
checked on Dec 3, 2024
Page view(s)
18
checked on Dec 3, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.