Observatorio de I+D+i UPM

Memorias de investigación
Research Publications in journals:
Homogeneous links and the Seifert matrix
Year:2012
Research Areas
  • Physics chemical and mathematical
Information
Abstract
Homogeneous links were introduced by Peter Cromwell, who pr oved that the projection surface of these links, that given by the Seifert al- gorithm, has minimal genus. Here we provide a different proof , with a geometric rather than combinatorial flavor. To do this, we fir st show a direct relation between the Seifert matrix and the decompo sition into blocks of the Seifert graph. Precisely, we prove that the Sei fert matrix can be arranged in a block triangular form, with small boxes in th e diagonal corresponding to the blocks of the Seifert graph. Then we pro ve that the boxes in the diagonal has non-zero determinant, by looking a t an explicit matrix of degrees given by the planar structure of the Seifer t graph. The paper contains also a complete classification of the homogen eous knots of genus one.
International
Si
JCR
No
Title
Pacific Journal of Mathematics
ISBN
0030-8730
Impact factor JCR
Impact info
Volume
255
DOI: 10.2140/pjm.2012.255.373
Journal number
2
From page
373
To page
392
Month
SIN MES
Ranking
Participants
  • Autor: Pedro Maria Gonzalez Manchon (UPM)
Research Group, Departaments and Institutes related
  • Creador: Departamento: Matemática Aplicada (E.U.I.T. Industrial)
S2i 2020 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)