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Matrix presentations of braids and applications


Author: Sang Youl Lee
Journal: Proc. Amer. Math. Soc. 127 (1999), 3403-3412
MSC (1991): Primary 57M25; Secondary 20F36
DOI: https://doi.org/10.1090/S0002-9939-99-04948-5
Published electronically: May 3, 1999
MathSciNet review: 1610737
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Abstract: We show that there exists a one-to-one correspondence between the class of certain block tridiagonal matrices with the entries $-1, 0,$ or $1$ and the free monoid generated by $2n$ generators $\sigma _{1}, \cdots ,\sigma _{n}, \sigma _{1}^{-1},\cdots , \sigma _{n}^{-1}$ and relation $\sigma _{i}^{\pm 1}\sigma _{j}^{\pm 1} = \sigma _{j}^{\pm 1}\sigma _{i}^{\pm 1}~ (|i-j| \geq 2)$ and give some applications for braids. In particular, we give new formulation of the reduced Alexander matrices for closed braids.


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Additional Information

Sang Youl Lee
Affiliation: Department of Mathematics, College of Natural Science, Kyungpook National University, Taegu 702-701, Korea
Address at time of publication: Department of Mathematics, Pusan National University, Pusan 609-735, Korea
Email: syleek@chollian.dacom.co.kr, syleek@chollian.net

DOI: https://doi.org/10.1090/S0002-9939-99-04948-5
Keywords: Alexander matrix, braid, nullity, signature
Received by editor(s): July 31, 1997
Received by editor(s) in revised form: January 26, 1998
Published electronically: May 3, 1999
Additional Notes: This research was supported by the Korea Science and Engineering Foundation.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1999 American Mathematical Society

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