The multi-variable Alexander polynomial of lens braids

Nafaa Chbili

doi:10.1142/S0218216502002189

The multi-variable Alexander polynomial of lens braids

Nafaa Chbili

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let n ≥ 2 be an integer and B_n the n-braid group. A braid β ∈ B_n is said to be a (p, s)-lens braid if there exists α ∈ B_n such that β=α^p(σ₁σ2₂ . . . σ_n-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.

Original language	English
Pages (from-to)	1323-1330
Number of pages	8
Journal	Journal of Knot Theory and its Ramifications
Volume	11
Issue number	8
DOIs	https://doi.org/10.1142/S0218216502002189
Publication status	Published - Dec 2002
Externally published	Yes

Keywords

Burau representation
Lens braids
Lens links
Multi-variable Alexander polynomial

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216502002189

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title = "The multi-variable Alexander polynomial of lens braids",

abstract = "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.",

keywords = "Burau representation, Lens braids, Lens links, Multi-variable Alexander polynomial",

author = "Nafaa Chbili",

note = "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.",

year = "2002",

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doi = "10.1142/S0218216502002189",

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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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DO - 10.1142/S0218216502002189

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SN - 0218-2165

VL - 11

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 8

ER -

The multi-variable Alexander polynomial of lens braids

Abstract

Keywords

ASJC Scopus subject areas

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