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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 15, 2015

On numerical invariants for knots in the solid torus

  • Khaled Bataineh
From the journal Open Mathematics

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.

References

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Received: 2015-8-31
Accepted: 2015-11-9
Published Online: 2015-12-15

©2015 Khaled Bataineh

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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