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Fibred knots and twisted Alexander invariants


Author: Jae Choon Cha
Journal: Trans. Amer. Math. Soc. 355 (2003), 4187-4200
MSC (2000): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9947-03-03348-8
Published electronically: June 24, 2003
MathSciNet review: 1990582
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Abstract: We study the twisted Alexander invariants of fibred knots. We establish necessary conditions on the twisted Alexander invariants for a knot to be fibred, and develop a practical method to compute the twisted Alexander invariants from the homotopy type of a monodromy. It is illustrated that the twisted Alexander invariants carry more information on fibredness than the classical Alexander invariants, even for knots with trivial Alexander polynomials.


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Additional Information

Jae Choon Cha
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Address at time of publication: Information and Communication University, 119 Munjiro, Yuseong-gu, Daejeon 305-714, Korea
Email: jccha@indiana.edu, jccha@icu.ac.kr

DOI: https://doi.org/10.1090/S0002-9947-03-03348-8
Keywords: Fibred knots, twisted Alexander invariants
Received by editor(s): October 5, 2001
Received by editor(s) in revised form: February 15, 2003
Published electronically: June 24, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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