On numerical invariants for knots in the solid torus
Open Mathematics (2015)
- Volume: 13, Issue: 1, page Article ID 1650051, 24 p.-Article ID 1650051, 24 p.
- ISSN: 2391-5455
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topKhaled Bataineh. "On numerical invariants for knots in the solid torus." Open Mathematics 13.1 (2015): Article ID 1650051, 24 p.-Article ID 1650051, 24 p.. <http://eudml.org/doc/275874>.
@article{KhaledBataineh2015,
abstract = {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.},
author = {Khaled Bataineh},
journal = {Open Mathematics},
keywords = {Bridge number of a knot; Solid torus; Universal cover; Vassiliev invariants; Gauss diagrams; modules; chord diagrams},
language = {eng},
number = {1},
pages = {Article ID 1650051, 24 p.-Article ID 1650051, 24 p.},
title = {On numerical invariants for knots in the solid torus},
url = {http://eudml.org/doc/275874},
volume = {13},
year = {2015},
}
TY - JOUR
AU - Khaled Bataineh
TI - On numerical invariants for knots in the solid torus
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - Article ID 1650051, 24 p.
EP - Article ID 1650051, 24 p.
AB - 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.
LA - eng
KW - Bridge number of a knot; Solid torus; Universal cover; Vassiliev invariants; Gauss diagrams; modules; chord diagrams
UR - http://eudml.org/doc/275874
ER -
References
top- [1] Milnor, J. W., On the Total Curvature of Knots, Ann. Math. 52, 248-257, 1950. [Crossref] Zbl0037.38904
- [2] Schubert, H., Uber eine numerische Knoteninvariante, Math. Z., 61 (1954), pp. 245–288. Zbl0058.17403
- [3] Hoste, J., Przytycki, J., An invariant of dichromatic links, Proc. Amer. Math. Soc., 105 (1989), 1003-1007. Zbl0687.57002
- [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. Zbl1220.57005
- [5] Cromwell, P. R., Knots and Links, Dover Publications, 2008.
- [6] Kawauchi, A., A Survey of Knot Theory, Birkhauser Verlag, 1996. Zbl0861.57001
- [7] Rolfsen, D., Knots and Links, Wilmington, DE: Publish or Perish Press, p. 115, 1976. Zbl0339.55004
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