Advertisement

Journal of Mathematical Chemistry

, Volume 40, Issue 2, pp 105–117 | Cite as

Twisted Surfaces

  • Victor A. Nicholson
Article

This article proves the laundry embedding theorem. It considers surface triples (S,G,J) in S 3 where S is a 2-manifold with boundary, G is a circle-with-chords, and J is an arc. The surfaces satisfy an embedding condition called laundry which is similar to being unknotted. The theorem gives elementary necessary and sufficient conditions for two triples to be equivalent by ambient isotopy. The theorem introduces a new topological invariant called turn. The surfaces of interest can arise from the augmented ribbon model of unknotted single domain protein.

Keywords

surface linking protein 

AMS subject classification

57M25 57M15 92C40 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nicholson V.A., and Maggiora G.M. (1992). J. Math. Chem. 11:47–63CrossRefGoogle Scholar
  2. 2.
    Gordon C.M., and Litherland R.A. (1978). Invent. Math. 47:53–69CrossRefGoogle Scholar
  3. 3.
    Lickorish W.B.R. (1997). An Introduction to Knot Theory, Grad. Texts in Math., vol. 175. Springer, New YorkGoogle Scholar
  4. 4.
    S. Naik and Stanford T., arXiv.math.GT/9911005 (1999).Google Scholar
  5. 5.
    Rushing T.B. (1973). Topological Embeddings, Pure and Applied Math., vol. 52 Academic Press, New YorkGoogle Scholar
  6. 6.
    Rourke C.P., and Sanderson B.J. (1982). Introduction to Piecewise-linear Topology. Springer, New YorkGoogle Scholar
  7. 7.
    Rolfsen D. (1976). Knots and Links. Publish or Perish, BerkeleyGoogle Scholar
  8. 8.
    Nicholson V.A., and Neuzil J.P. (1993). J. Math. Chem. 12:53–58CrossRefGoogle Scholar
  9. 9.
    Suzuki S. (1977). Canad. J. Math. 29:111–124Google Scholar
  10. 10.
    Nicholson V. (1995). Graph Theory, Combinatorics, and Applications. Wiley, New York, pp. 833–838Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA

Personalised recommendations