TY - JOUR
T1 - The multi-variable Alexander polynomial of lens braids
AU - Chbili, Nafaa
N1 - Funding Information:
This work was partially completed when I was visiting the University of Toronto supported by a NSERC grant. I would like to express my thanks and gratitude to Professor K. Murasugi for his hospitality and for many valuable comments.
PY - 2002/12
Y1 - 2002/12
N2 - Let n ≥ 2 be an integer and Bn the n-braid group. A braid β ∈ Bn is said to be a (p, s)-lens braid if there exists α ∈ Bn such that β=αp(σ1σ22 . . . σn-1)ns. In this paper we use the multi-variable Alexander polynomial to find a necessary condition for a braid to be a (p, s)-lens braid, for p prime. Our main tool here is the multi-variable Burau representation of the n-braid group.
AB - Let n ≥ 2 be an integer and Bn the n-braid group. A braid β ∈ Bn is said to be a (p, s)-lens braid if there exists α ∈ Bn such that β=αp(σ1σ22 . . . σn-1)ns. In this paper we use the multi-variable Alexander polynomial to find a necessary condition for a braid to be a (p, s)-lens braid, for p prime. Our main tool here is the multi-variable Burau representation of the n-braid group.
KW - Burau representation
KW - Lens braids
KW - Lens links
KW - Multi-variable Alexander polynomial
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U2 - 10.1142/S0218216502002189
DO - 10.1142/S0218216502002189
M3 - Article
AN - SCOPUS:0036967060
SN - 0218-2165
VL - 11
SP - 1323
EP - 1330
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 8
ER -