Skip to main content
SpringerLink
Log in

Invariants of graphs and their applications to knot theory

  • Survey Articles
  • Conference paper
  • First Online:
Algebraic Topology Poznań 1989

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1474))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci., U.S.A., 9 (1923) 93–95.

    Article  Google Scholar 

  2. C. Bankwitz, Über die Torsionzahlen der alternierenden Knoten, Math. Ann. 103 (1930) 145–161.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Frank-R.F. Williams, Braids and the Jones polynomial, Trans. Amer. Math. Soc. 303 (1987) 97–108.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Freyd, et al., A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. 12 (1985) 103–111.

    Article  MathSciNet  Google Scholar 

  5. C. McA Gordon-R.A. Litherland, On the signature of a link, Invent. Math. 47 (1978) 53–69

    Article  MathSciNet  MATH  Google Scholar 

  6. C. McA Gordon-J. Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 3 (1989), 371–415.

    Article  MathSciNet  MATH  Google Scholar 

  7. V.F.R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335–388.

    Article  MathSciNet  MATH  Google Scholar 

  8. L.H. Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395–407.

    Article  MathSciNet  MATH  Google Scholar 

  9. W.B.R. Lickorish-K.C. Millett, A polynomial invariant of oriented links, Topology 26 (1987) 107–141.

    Article  MathSciNet  MATH  Google Scholar 

  10. H.R. Morton, Seifert circles and knot polynomials, Math. Proc. Cambridge. Phil. Soc. 99 (1986) 107–109

    Article  MathSciNet  MATH  Google Scholar 

  11. H.R. Morton-H.B. Short, The 2-variable polynomial of cable knots, Math. Proc. Cambridge Phil. Soc. 101 (1987), 267–278.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387–422.

    Article  MathSciNet  MATH  Google Scholar 

  13. —, Jones polynomials and classical conjecture in knot theory, Topology 26 (1987) 187–194.

    Article  MathSciNet  MATH  Google Scholar 

  14. —, Jones polynomials and classical conjecture in knot theory (II), Math. Proc. Cambridge Phil. Soc. 102 (1987) 317–318.

    Article  MathSciNet  MATH  Google Scholar 

  15. —, On invariants of graphs with applications to knot theory, Trans. Amer. Math. Soc. 314 (1989) 1–49.

    Article  MathSciNet  MATH  Google Scholar 

  16. —, On the signature of a graph. C.R. Math. Rep. Acad. Sci. Canada 10 (1988) 107–111.

    MathSciNet  MATH  Google Scholar 

  17. —, On the braid index of alternating links, (to appear in Trans. Amer. Math. Soc.).

    Google Scholar 

  18. K. Murasugi-J.H.Przytycki, The index of a graph with applications to knot theory (preprint)

    Google Scholar 

  19. J.H. Przytycki-P. Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1987) 115–139.

    MathSciNet  MATH  Google Scholar 

  20. D. Rolfsen, Knots and links, Publish or Perish Inc (1976).

    Google Scholar 

  21. M. Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987) 287–309.

    Article  MathSciNet  MATH  Google Scholar 

  22. , Kauffman's polynomial and alternating links, Topology 27 (1988) 311–318.

    Article  MathSciNet  MATH  Google Scholar 

  23. —, On flypes and alternating tangles, (preprint).

    Google Scholar 

  24. P.Traczyk, On the index of graphs: Index versus cycle index (preprint)

    Google Scholar 

  25. H. Whitney, 2-isomorphic graphs, Amer. J. Math. 55 (1933) 236–244.

    Article  MathSciNet  MATH  Google Scholar 

  26. S. Yamada, The minimal number of Seifert circles equals the braid index of a link, Inv. math. 89 (1987) 347–356.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Toronto, M5S 1A1, Toronto, Ontario

    Kunio Murasugi

Authors
  1. Kunio Murasugi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Stefan Jackowski Bob Oliver Krzystof Pawałowski

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Murasugi, K. (1991). Invariants of graphs and their applications to knot theory. In: Jackowski, S., Oliver, B., Pawałowski, K. (eds) Algebraic Topology Poznań 1989. Lecture Notes in Mathematics, vol 1474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084739

Download citation

  • DOI: https://doi.org/10.1007/BFb0084739

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54098-4

  • Online ISBN: 978-3-540-47403-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation