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Linking Number of Singular Links and the Seifert Matrix

Published online by Cambridge University Press:  20 November 2018

James J. Hebda ,
Chun-Chung Hsieh  and
Chichen M. Tsau
James J. Hebda
Affiliation:
Institute of Mathematics, Academia Sinica, Taiwan, R. O. Chinae-mail: macchsieh@ccvax.sinica.edu.tw
Chun-Chung Hsieh
Affiliation:
Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, U.S.A. e-mail: hebdajj@slu.edutsaumc@slu.edu
Chichen M. Tsau
Affiliation:
Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, U.S.A. e-mail: hebdajj@slu.edutsaumc@slu.edu
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Abstract

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We extend the notion of linking number of an ordinary link of two components to that of a singular link with transverse intersections, in which case the linking number is a half-integer. We then apply it to simplify the construction of the Seifert matrix, and therefore the Alexander polynomial, in a natural way.

Keywords

57M25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 3 , 01 September 2007 , pp. 390 - 398
Copyright
Copyright © Canadian Mathematical Society 2007

References

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