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A generalized Burau
representation for string links
Daniel S. Silver and Susan G. Williams |
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Vol. 197 (2001), No. 1, 241–255
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Abstract |
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A 2-variable matrix ℬ∈ GLn(Z[u±1,v±1]) is defined for any n-string link, generalizing the Burau matrix of an n-braid. The specialization u = 1,v = t−1 recovers the generalized Burau matrix recently defined by X. S. Lin, F. Tian and Z. Wang using probabilistic methods. The specialization u = t−1,v = 1 results in a matrix with a natural algebraic interpretation, and one that yields homological information about the complement of the closed string link. |
Milestones
Received: 3 January 1999
Revised: 28 February 1999
Published: 1 January 2001
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Authors |
| Daniel S. Silver | |
| Department of Mathematics and
Statistics University of South Alabama Mobile, AL 36688 |
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| Susan G. Williams | |
| University of South Alabama Mobile, AL 36688 |
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