The 1,2-coloured HOMFLY-PT link homology
HTML articles powered by AMS MathViewer
- by Marco Mackaay, Marko Stošić and Pedro Vaz
- Trans. Amer. Math. Soc. 363 (2011), 2091-2124
- DOI: https://doi.org/10.1090/S0002-9947-2010-05155-4
- Published electronically: November 17, 2010
- PDF | Request permission
Abstract:
In this paper we define the 1,2-coloured HOMFLY-PT triply graded link homology and prove that it is a link invariant. We also conjecture on how to generalize our construction for arbitrary colours.References
- D. J. Benson, Representations and cohomology. I, Cambridge Studies in Advanced Mathematics, vol. 30, Cambridge University Press, Cambridge, 1991. Basic representation theory of finite groups and associative algebras. MR 1110581
- Xiao-Wu Chen, Yu Ye, and Pu Zhang, Algebras of derived dimension zero, Comm. Algebra 36 (2008), no. 1, 1–10. MR 2378361, DOI 10.1080/00927870701649184
- W. Fulton, Equivariant cohomology in algebraic geometry, Eilenberg lectures, Columbia University, spring 2007, available at http://www.math.lsa.umich.edu/ dandersn/eilenberg/.
- S. Gukov, A. Iqbal, C. Kozcaz, C. Vafa, Link Homologies and the Refined Topological Vertex, preprint 2007, arXiv:0705.1368.
- M-J. Jeong and D. Kim, Quantum $sl(n,\mathbb {C})$ link invariants, preprint 2005, arXiv: math /0506403v2 [math.GT].
- Mikhail Khovanov, Triply-graded link homology and Hochschild homology of Soergel bimodules, Internat. J. Math. 18 (2007), no. 8, 869–885. MR 2339573, DOI 10.1142/S0129167X07004400
- Mikhail Khovanov and Lev Rozansky, Matrix factorizations and link homology, Fund. Math. 199 (2008), no. 1, 1–91. MR 2391017, DOI 10.4064/fm199-1-1
- Mikhail Khovanov and Lev Rozansky, Matrix factorizations and link homology. II, Geom. Topol. 12 (2008), no. 3, 1387–1425. MR 2421131, DOI 10.2140/gt.2008.12.1387
- Hitoshi Murakami, Tomotada Ohtsuki, and Shuji Yamada, Homfly polynomial via an invariant of colored plane graphs, Enseign. Math. (2) 44 (1998), no. 3-4, 325–360. MR 1659228
- J. Rasmussen, Some differentials on Khovanov-Rozansky homology, preprint 2006, arXiv: math/0607544v2 [math.GT].
- M. Stošić, Hochschild homology of certain Soergel bimodules, preprint 2008, arXiv:0810.3578.
- R. G. Swan, Algebraic $K$-theory, Lecture Notes in Mathematics, No. 76, Springer-Verlag, Berlin-New York, 1968. MR 0245634
- Ben Webster and Geordie Williamson, A geometric model for Hochschild homology of Soergel bimodules, Geom. Topol. 12 (2008), no. 2, 1243–1263. MR 2425548, DOI 10.2140/gt.2008.12.1243
- B Webster, G Williamson A geometric construction of colored HOMFLYPT homology, preprint 2009, arXiv:0905.0486.
- H. Wu, Matrix factorizations and colored MOY graphs, preprint 2008, arXiv:0803.2071v3 [math.GT].
- Y. Yonezawa, Matrix factorizations and intertwiners of the fundamental representations of quantum group $U_q(sl_n)$, preprint 2008, arXiv:0806.4939v1 [math.QA].
Bibliographic Information
- Marco Mackaay
- Affiliation: Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal – and – CAMGSD, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
- MR Author ID: 648267
- Email: mmackaay@ualg.pt
- Marko Stošić
- Affiliation: Instituto de Sistemas e Robótica and CAMGSD, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
- Email: mstosic@math.ist.utl.pt
- Pedro Vaz
- Affiliation: Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal – and – CAMGSD, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
- Address at time of publication: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- Email: pfortevaz@ualg.pt, pedro.vaz@math.uzh.ch
- Received by editor(s): December 2, 2008
- Received by editor(s) in revised form: July 2, 2009
- Published electronically: November 17, 2010
- Additional Notes: The authors thank Mikhail Khovanov and Catharina Stroppel for helpful conversations on the topic of this paper. The authors were supported by the Fundação para a Ciência e a Tecnologia (ISR/IST plurianual funding) through the programme “Programa Operacional Ciência, Tecnologia, Inovação” (POCTI) and the POS Conhecimento programme, cofinanced by the European Community fund FEDER. The second author was also partially supported by the Ministry of Science of Serbia, project 144032
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 2091-2124
- MSC (2010): Primary 18G60, 57M27
- DOI: https://doi.org/10.1090/S0002-9947-2010-05155-4
- MathSciNet review: 2746676