Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-18T06:25:14.274Z Has data issue: false hasContentIssue false
  • English
  • Français

Connect sum and transversely non simple knots

Published online by Cambridge University Press:  01 May 2009

KEIKO KAWAMURO
KEIKO KAWAMURO*
Affiliation:
Department of Mathematics, Rice University, Houston, TX 77005, U.S.A. e-mail: kk6@rice.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that transversal non-simplicity is preserved under taking connect sum, generalizing Veŕtesi's result [11].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 3 , May 2009 , pp. 661 - 669
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bennequin, D. Entrelacements et équations de Pfaff. Astérisque. 107–108 (1983), 87–161.Google Scholar
[2]Birman, J. S. and Menasco, W. W.Studying links via closed braids. IV. Composite links and split links. Invent. Math. 102 (1990), no. 1, 115–139.CrossRefGoogle Scholar
[3]Birman, J. S. and Menasco, W. W.Studying links via closed braids. V. The unlink. Trans. Amer. Math. Soc. 329 (1992), no. 2, 585–606.Google Scholar
[4]Birman, J. S. and Menasco, W. W.Stabilization in the braid groups. II. Transversal simplicity of knots. Geom. Topol. 10 (2006), 1425–1452CrossRefGoogle Scholar
[5]Birman, J. S. and Wrinkle, N. C.On transversally simple knots. J. Diff. Geom. 55 (2000), no. 2, 325–354.Google Scholar
[6]Epstein, J., Fuchs, D. and Meyer, M.Chekanov–Eliashberg invariants and transverse approximations of Legendrian knots. Pacific J. Math. 201 (2001), no. 1, 89–106.Google Scholar
[7]Etnyer, J. and Honda, K.On connected sums and Legendrian knots. Adv. Math. 179 (2003), no. 1, 59–74.CrossRefGoogle Scholar
[8]Etnyer, J. Legendrian and transversal knots. Handbook of Knot Theory. (Elsevier B. V., Amsterdam, 2005), 105–185.CrossRefGoogle Scholar
[9]Ng, L., Ozsvath, P. and Thurston, D. Transverse knots distinguished by knot floer homology. math.GT/0703446.Google Scholar
[10]Orevkov, S. Y. and Shevchishin, V. V.Markov theorem for transversal links. J. Knot Theory Ramifications 12 (2003), no. 7, 905–913.CrossRefGoogle Scholar
[11]Veŕtesi, V. Transversely non simple knots. arXiv:0712.2803v2.Google Scholar
[12]Wrinkle, N. C. The Markov theorem for transverse knots. math.GT/0202055.Google Scholar