On numerical invariants for knots in the solid torus

• Autorzy: Khaled Bataineh
• Języki publikacji: EN

Abstrakty

EN

We define some new numerical invariants for knots with zero winding number in the solid torus. These invariants explore some geometric features of knots embedded in the solid torus. We characterize these invariants and interpret them on the level of the knot projection. We also find some relations among some of these invariants. Moreover, we give lower bounds for some of these invariants using Vassiliev invariants of type one. We connect our invariants to the bridge number in the solid torus. We give a lower bound and an upper bound of the wrap of a knot in the solid torus in terms of our new invariants.

Słowa kluczowe

EN

Bridge number of a knot; Solid torus; Universal cover; Vassiliev invariants

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-08-31

zaakceptowano

2015-11-09

online

2015-12-15

Twórcy

autor

Khaled Bataineh

• Department of Mathematics and Statistics, Jordan University of Science and Technology,
  Irbid, Jordan

Bibliografia

• [1] Milnor, J. W., On the Total Curvature of Knots, Ann. Math. 52, 248-257, 1950. [Crossref]
• [2] Schubert, H., Uber eine numerische Knoteninvariante, Math. Z., 61 (1954), pp. 245–288.
• [3] Hoste, J., Przytycki, J., An invariant of dichromatic links, Proc. Amer. Math. Soc., 105 (1989), 1003-1007.
• [4] Bataineh, K., Abu Zaytoon, M., Vassiliev invariants of type one for links in the solid torus, Topology and its applications, 157 (2010) pp. 2495-2504.
• [5] Cromwell, P. R., Knots and Links, Dover Publications, 2008.
• [6] Kawauchi, A., A Survey of Knot Theory, Birkhauser Verlag, 1996.
• [7] Rolfsen, D., Knots and Links, Wilmington, DE: Publish or Perish Press, p. 115, 1976.

Identyfikatory

DOI

10.1515/math-2015-0084