Repositorio de producción científica de la Universidad de Sevilla

Closures of positive braids and the Morton-Franks-Williams inequality

 

Advanced Search
 
Opened Access Closures of positive braids and the Morton-Franks-Williams inequality
Cites

Show item statistics
Icon
Export to
Author: González-Meneses López, Juan
González Manchón, Pedro María
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2014-09-01
Published in: Topology and its Applications, 174 (1), 14-24.
Document type: Article
Abstract: We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is a orthonormal basis for the inner product of the Hecke algebra of the braid group defined by K´alm´an, who first obtained this result by using an interesting connection with Contact Topology. We also introduce a new technique to study the Homflypt polynomial for closures of positive braids, namely resolution trees whose leaves are simple braids. In terms of these simple resolution trees, we characterize closed positive braids for which the Morton-Franks-Williams inequality is strict. In particular, we determine explicitly the positive braid words on three strands whose closures have braid index three.
Cite: González-Meneses López, J. y González Manchón, P.M. (2014). Closures of positive braids and the Morton-Franks-Williams inequality. Topology and its Applications, 174 (1), 14-24.
Size: 180.9Kb
Format: PDF

URI: http://hdl.handle.net/11441/42291

DOI: http://dx.doi.org/10.1016/j.topol.2014.06.008

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)