68
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

On Odd Torsion in Even Khovanov Homology

ORCID Icon

References

  • Asaeda, M. M, Przytycki, J. H. (2004). Khovanov homology: torsion and thickness Advances in Topological Quantum Field Theory, 135–166. NATO Sci. Ser. II Math. Phys. Chem., 179, Dordrecht: Kluwer Acad. Publ.
  • Bar-Natan, D. (2002). On Khovanov’s categorification of the Jones polynomial. Algebr. Geom. Topol. 2(1): 337–370. doi:10.2140/agt.2002.2.337
  • Chandler, A., Lowrance, A., Sazdanović, R, Summers, V. Torsion in thin regions of Khovanov homology. Preprint https://arxiv.org/abs/1903.05760.
  • Jones, V. F. R. (1985). A polynomial invariant for knots via von Neumann algebras. Bull. Amer. Math. Soc. 12(1): 103–111. doi:10.1090/S0273-0979-1985-15304-2
  • Kauffman, L. H. (1987). State models and the Jones polynomial. Topology 26(3): 395–407. doi:10.1016/0040-9383(87)90009-7
  • Khovanov, M. (2000). A categorification of the Jones polynomial. Duke Math. J. 101(3): 359–426. doi:10.1215/S0012-7094-00-10131-7
  • Kronheimer, P. B, Mrowka, T. S. (2011). Khovanov homology is an unknot-detector. Publmathihes. 113(1): 97–208. doi:10.1007/s10240-010-0030-y
  • Mukherjee, S., Przytycki, J. H., Silvero, M., Wang, X, Yang, S. Y. (2018). Search for Torsion in Khovanov Homology. Exp. Math 27(4): 488–497. doi:10.1080/10586458.2017.1320242
  • Mukherjee, S. (2019). On Skein Modules and homology theories related to knot theory. Ph.D. thesis. The George Washington University. 124pp. Available at: https://pqdtopen.proquest.com/pubnum/13810465.html).
  • Murasugi, K. (1974). On closed 3-braids. Memoirs of the American Mathmatical Society, No. 151. Providence, RI: American Mathematical Society.
  • Przytycki, J. H, Sazdanović, R. (2014). Torsion in Khovanov homology of semi-adequate links. Fund. Math. 225(1): 277–304. doi:10.4064/fm225-1-13
  • Rasmussen, J. (2005). Knot polynomials and knot homologies. In Geometry and topology of manifolds 261–280. Fields Inst. Commun., 47. Providence, RI: Amer. Math. Soc. https://bookstore.ams.org/fic-47/.
  • Schütz, D. Torsion calculations in Khovanov cohomology (in preparation). http://maths.dur.ac.uk/∼dma0ds/
  • Shumakovitch, A. N. (2014). Torsion of Khovanov homology. Fund. Math. 225(1): 343–364. doi:10.4064/fm225-1-16
  • Turner, P. (2017). Five lectures on Khovanov homology. J. Knot Theory Ramifications 26(3): 41pp., 1741009. doi:10.1142/S0218216517410097
  • Viro, O. (2004). Khovanov homology, its definitions and ramifications. Fund. Math. 184: 317–342. doi:10.4064/fm184-0-18
  • Watson, L. (2007). Knots with identical Khovanov homology. Algebr. Geom. Topol. 7(3): 1389–1407. doi:10.2140/agt.2007.7.1389

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.