Journal article
The algebraic crossing number and the braid index of knots and links
Algebraic & geometric topology, Vol.6(5), pp.2313-2350
07/06/2009
DOI: 10.2140/agt.2006.6.2313
Abstract
Algebr. Geom. Topol. 6 (2006) 2313-2350 It has been conjectured that the algebraic crossing number of a link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower bound for braid index. And sharpness of the inequality on a knot type implies the truth of the conjecture for the knot type. We prove that there are infinitely many examples of knots and links for which the inequality is not sharp but the conjecture is still true. We also show that if the conjecture is true for K and L, then it is also true for the (p,q)-cable of K and for the connect sum of K and L.
Details
- Title: Subtitle
- The algebraic crossing number and the braid index of knots and links
- Creators
- Keiko Kawamuro
- Resource Type
- Journal article
- Publication Details
- Algebraic & geometric topology, Vol.6(5), pp.2313-2350
- DOI
- 10.2140/agt.2006.6.2313
- ISSN
- 1472-2747
- eISSN
- 1472-2739
- Language
- English
- Date published
- 07/06/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9983985975902771
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