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CHORD DIAGRAMS AND COXETER LINKS

Published online by Cambridge University Press:  28 January 2004

ERIKO HIRONAKA
ERIKO HIRONAKA
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USAhironaka@math.fsu.edu
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Abstract

The paper presents a construction of fibered links $(K, \Sigma)$ out of chord diagrams $\sL$. Let $\Gamma$ be the incidence graph of $\sL$. Under certain conditions on $\sL$ the symmetrized Seifert matrix of $(K, \Sigma)$ equals the bilinear form of the simply-laced Coxeter system $(W, S)$ associated to $\Gamma$; and the monodromy of $(K, \Sigma)$ equals minus the Coxeter element of $(W, S)$. Lehmer's problem is solved for the monodromy of these Coxeter links.

Keywords

57M2751F15
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 243 - 257
Copyright
The London Mathematical Society 2004

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