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

Gonzalez Meneses, Juan and Gonzalez Manchon, Pedro Maria (2014). Closures of positive braids and the Morton-Franks-Williams inequality. "Topology and its Applications", v. 174 ; pp. 14-24. ISSN 0166-8641. https://doi.org/10.1016/j.topol.2014.06.008.

Description

Title: Closures of positive braids and the Morton-Franks-Williams inequality
Author/s:
  • Gonzalez Meneses, Juan
  • Gonzalez Manchon, Pedro Maria
Item Type: Article
Título de Revista/Publicación: Topology and its Applications
Date: September 2014
ISSN: 0166-8641
Volume: 174
Subjects:
Freetext Keywords: Positive braid; Morton–Franks–Williams inequality; Homflypt polynomial; Braid index
Faculty: E.T.S.I. Diseño Industrial (UPM)
Department: Matemática Aplicada a la Ingeniería Industrial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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 an orthonormal basis for the inner product of the Hecke algebra of the braid group defined by Kálmán, 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.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2010-19355UnspecifiedJuan González-Meneses LópezPropiedades algebraicas y topológicas de trenzas y nudos

More information

Item ID: 40165
DC Identifier: http://oa.upm.es/40165/
OAI Identifier: oai:oa.upm.es:40165
DOI: 10.1016/j.topol.2014.06.008
Official URL: http://www.sciencedirect.com/science/article/pii/S0166864114002612
Deposited by: Memoria Investigacion
Deposited on: 05 May 2016 07:53
Last Modified: 30 Sep 2016 22:30
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