Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Diagrams of divide links


Author: Sergei Chmutov
Journal: Proc. Amer. Math. Soc. 131 (2003), 1623-1627
MSC (2000): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-02-06770-9
Published electronically: October 15, 2002
MathSciNet review: 1950295
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Recently N. A'Campo suggested a construction of a link from a generic immersion of a curve into a 2-disk. It is tightly related to the singularity theory. In this paper, we give a simple procedure to draw a diagram of the link from a picture of the curve.


References [Enhancements On Off] (What's this?)

  • 1. N. A'Campo, Le groupe de monodromie du déploiement des singularités isolées de courbes planes I, Math. Ann., 213 (1975) 1-32. MR 51:13282
  • 2. N. A'Campo, Real deformations and complex topology of plane curve singularities, Ann. Fac. Sci. Toulouse Math. (6) 8 (1999), no. 1, 5-23 (see also alg-geom/9710023). MR 2001d:32043a
  • 3. N. A'Campo, Generic immersions of curves, knots, monodromy and gordian number, Inst. Hautes Etudes Sci. Publ. Math. No. 88 (1998), 151-169 (1999) (see also math.GT/9803081). MR 2001b:57009
  • 4. N. A'Campo, Private communication, January, 2001.
  • 5. V. I. Arnold, Topological invariants of plane curves and caustics, University Lecture Series, Vol. 5, AMS, Providence, RI, 1994. MR 95h:57003
  • 6. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, Vol. II, Birkhäuser, Boston, MA, 1988. MR 89g:58024
  • 7. W. Burau, Kennzeichnung der Schlauchknoten, Abh. Math. Sem. Univ. Hamburg, 9 (1932) 125-133.
  • 8. O. Couture, B. Perron, Representative braids for links associated to plane immersed curves, Journal of Knot Theory and Its Ramifications, 9 (2000) 1-30. MR 2001b:57012
  • 9. S. M. Gusein-Zade, Intersection matrices for certain singularities of functions of two variables, Functional Anal. and its Appl., 8 (1974) 11-15. MR 49:3202
  • 10. M. Hirasawa, Visualization of A'Campo's fibered links and unknotting operations, to appear in Topology and its Applications.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M25

Retrieve articles in all journals with MSC (2000): 57M25


Additional Information

Sergei Chmutov
Affiliation: Department of Mathematics, The Ohio State University at Mansfield, 1680 University Drive, Mansfield, Ohio 44906
Email: chmutov@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06770-9
Keywords: Links, fibered links, link diagram, divide.
Received by editor(s): November 19, 2001
Received by editor(s) in revised form: December 17, 2001
Published electronically: October 15, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society