The Jones polynomial, genus and weak genus of a knot

A. Stoimenow

Annales de la Faculté des sciences de Toulouse : Mathématiques (1999)

  • Volume: 8, Issue: 4, page 677-693
  • ISSN: 0240-2963

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Stoimenow, A.. "The Jones polynomial, genus and weak genus of a knot." Annales de la Faculté des sciences de Toulouse : Mathématiques 8.4 (1999): 677-693. <http://eudml.org/doc/73504>.

@article{Stoimenow1999,
author = {Stoimenow, A.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Seifert genus},
language = {eng},
number = {4},
pages = {677-693},
publisher = {UNIVERSITE PAUL SABATIER},
title = {The Jones polynomial, genus and weak genus of a knot},
url = {http://eudml.org/doc/73504},
volume = {8},
year = {1999},
}

TY - JOUR
AU - Stoimenow, A.
TI - The Jones polynomial, genus and weak genus of a knot
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1999
PB - UNIVERSITE PAUL SABATIER
VL - 8
IS - 4
SP - 677
EP - 693
LA - eng
KW - Seifert genus
UR - http://eudml.org/doc/73504
ER -

References

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  1. [Ad] Adams ( C.C.). - The knot book, W. H. Freeman & Co., New York, 1994. Zbl0840.57001
  2. [BFK] Bullock ( D.), Frohman ( C.) and Kania-Bartoszynska ( J.). - Understanding the Kauffman bracket skein module, q-alg 9604013. 
  3. [Ga] Gabai ( D.). — Genera of the alternating links, Duke Math. J.53 (3) (1986), 677-681. Zbl0631.57004MR860665
  4. [H] Freyd ( P.), Hoste ( J.), Lickorish ( W.B.R.), Millett ( K.), Ocneanu ( A.) and Yetter ( D.). — A new polynomial invariant of knots and links, Bull. Amer. Math. Soc.12 (1985), 239-246. Zbl0572.57002MR776477
  5. [HTW] Hoste ( J.), Thistlethwaite ( M.) and Weeks ( J.). - The first 1,701,936 knots, Math. Intell.20 (4) (1998), 33-48. Zbl0916.57008MR1646740
  6. [J] Jones ( V.F.R.). - A polynomial invariant of knots and links via von Neumann algebras, Bull. Amer. Math. Soc.12 (1985), 103-111. Zbl0564.57006MR766964
  7. [J2] Jones ( V.F.R.). - Hecke algebra representations of braid groups and link polynomials, Ann. of Math.126 (1987) 335-388. Zbl0631.57005MR908150
  8. [Ka] Kauffman ( L.H.). - State models and the Jones polynomial, Topology26 (1987), 395-407. Zbl0622.57004MR899057
  9. [Ka2] Kauffman ( L.H.). - New invariants in the theory of knots, Amer. Math. Mon.3 (1988), 195-242. Zbl0657.57001MR935433
  10. [Ka3] Kauffman ( L.H.). - An invariant of regular isotopy, Trans. Amer. Math. Soc.318 (1990), 417-471. Zbl0763.57004MR958895
  11. [LT] Lickorish ( W.B.R.) and Thistlethwaite ( M.B.). - Some links with non-trivial polynomials and their crossing numbers, Comment. Math. Helv.63 (1988), 527-539. Zbl0686.57002MR966948
  12. [Mo] Morton ( H.R.). - Seifert circles and knot polynomials, Proc. Camb. Phil. Soc.99 (1986), 107-109. Zbl0588.57008MR809504
  13. [Mu] Murasugi ( K.). - Jones polynomial and classical conjectures in knot theory, Topology26 (1987), 187-194. Zbl0628.57004MR895570
  14. [St] Stoimenow ( A.). - Knots of genus two, preprint. 
  15. [St2] Stoimenow ( A.). - Knots of genus one, accepted by Proc. Amer. Math. Soc. MR1825928
  16. [St3] Stoimenow ( A.). - The polynomial behaviour of some knot invariants, preprint. MR1911864
  17. [St4] Stoimenow ( A.). - Gauß sum invariants, Vassiliev invariants and braiding sequences, to appear in Jour. of Knot Theory and its Ramifications. Zbl0998.57032MR1749498
  18. [St5] Stoimenow ( A.). - Polynomials of knots with up to 10 crossings, tables available on my webpage. 
  19. [St6] Stoimenow ( A.). - On some restrictions to the values of the Jones polynomial, Humboldt UniversityBerlin preprint, October 1998. 
  20. [St7] Stoimenow ( A.). - Positive knots, closed braids and the Jones polynomial, preprint. math/9805078. MR2004964
  21. [Th] Thistlethwaite ( M.B.). - A spanning tree expansion for the Jones polynomial, Topology26 (1987), 297-309. Zbl0622.57003MR899051

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