Homogeneous links and the Seifert matrix

Gonzalez Manchon, Pedro Maria (2012). Homogeneous links and the Seifert matrix. "Pacific Journal of Mathematics", v. 255 (n. 2); pp. 373-392. ISSN 0030-8730. https://doi.org/10.2140/pjm.2012.255.373.

Description

Title: Homogeneous links and the Seifert matrix
Author/s:
  • Gonzalez Manchon, Pedro Maria
Item Type: Article
Título de Revista/Publicación: Pacific Journal of Mathematics
Date: 10 April 2012
ISSN: 0030-8730
Volume: 255
Subjects:
Freetext Keywords: homogeneous link, projection surface, Seifert graph, Seifert matrix, Conway polynomial, knot genus, blocks of a graph
Faculty: E.U.I.T. Industrial (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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.

More information

Item ID: 22641
DC Identifier: http://oa.upm.es/22641/
OAI Identifier: oai:oa.upm.es:22641
DOI: 10.2140/pjm.2012.255.373
Official URL: http://msp.org/pjm/2012/255-2/p06.xhtml
Deposited by: Memoria Investigacion
Deposited on: 20 Mar 2014 11:03
Last Modified: 21 Apr 2016 17:37
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