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 nonzero 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

00308730 
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
