|
Braids, transversal links and the Khovanov-Rozansky Theory
Author(s):
Hao
Wu
Journal:
Trans. Amer. Math. Soc.
360
(2008),
3365-3389.
MSC (2000):
Primary 57M25, 57R17
Posted:
February 27, 2008
MathSciNet review:
2386230
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We establish some inequalities for the Khovanov-Rozansky cohomologies of braids. These give new upper bounds of the self-linking numbers of transversal links in standard contact  which are sharper than the well-known bound given by the HOMFLY polynomial. We also introduce a sequence of transversal link invariants and discuss some of their properties.
References:
-
- 1.
- D. Bar-Natan, Khovanov's homology for tangles and cobordisms, Algebr. Geom. Topol. 9 (2005), 1443-1499 (electronic). MR 2174270 (2006g:57017)
- 2.
- D. Bennequin, Entrelacements et équations de Pfaff, Astérisque 107-108 (1983), 87-161. MR 753131 (86e:58070)
- 3.
- E. Ferrand, On Legendrian knots and polynomial invariants, Proc. Amer. Math. Soc. 130 (2002), no. 4, 1169-1176 (electronic). MR 1873793 (2002j:57047)
- 4.
- J. Franks, R. F. Williams, Braids and the Jones polynomial, Trans. Amer. Math. Soc. 303 (1987), no. 1, 97-108. MR 896009 (88k:57006)
- 5.
- D. Fuchs, S. Tabachnikov, Invariants of Legendrian and transverse knots in the standard contact space, Topology 36 (1997), no. 5, 1025-1053. MR 1445553 (99a:57006)
- 6.
- M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000), no. 3, 359-426. MR 1740682 (2002j:57025)
- 7.
- M. Khovanov, L. Rozansky, Matrix factorizations and link homology, arXiv:math.QA/ 0401268.
- 8.
- M. Khovanov, L. Rozansky, Matrix factorizations and link homology II, arXiv:math.QA/ 0505056.
- 9.
- H. Morton, Seifert circles and knot polynomials, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 1, 107-109. MR 809504 (87c:57006)
- 10.
- S. Orevkov, V. Shevchishin, Markov theorem for transversal links, J. Knot Theory Ramifications 12 (2003), no. 7, 905-913. MR 2017961 (2004j:57011)
- 11.
- O. Plamenevskaya, Transverse knots and Khovanov homology, Math. Res. Lett. 13 (2006), 571-586. MR 2250492 (2007d:57043)
- 12.
- N. Wrinkle, The Markov Theorem for transverse knots, arXiv:math.GT/0202055.
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
57M25, 57R17
Retrieve articles in all Journals with
MSC (2000):
57M25, 57R17
Additional Information:
Hao
Wu
Affiliation:
Department of Mathematics and Statistics, Lederle Graduate Research Tower, 710 North Pleasant Street, University of Massachusetts, Amherst, Massachusetts 01003-9305
Address at time of publication:
Department of Mathematics, The George Washington University, Monroe Hall, Room 240, 2115 G Street, N.W., Washington, DC 20052
Email:
wu@math.umass.edu, haowu@gwu.edu
DOI:
10.1090/S0002-9947-08-04339-0
PII:
S 0002-9947(08)04339-0
Keywords:
Braid,
transversal knot,
knot homology,
matrix factorization
Received by editor(s):
January 20, 2006
Received by editor(s) in revised form:
May 24, 2006
Posted:
February 27, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
