The Alexander Polynominal for Virtual Twist Knots

Isaac Benioff; Blake Mellor

doi:10.1142/S0218216517500079

The Alexander Polynominal for Virtual Twist Knots

Isaac Benioff, Blake Mellor

Mathematics, Statistics and Data Science

Williams College

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

Abstract

We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial Δ0 (as defined by Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications12 (2003) 987–1000]) of these virtual twist knots. These results are applied to provide evidence for a conjecture that the odd writhe of a virtual knot can be obtained from Δ0 .

Original language	English
Article number	1750007
Number of pages	23
Journal	Journal of Knot Theory and its Ramifications
Volume	26
Issue number	1
DOIs	https://doi.org/10.1142/S0218216517500079
State	Published - Jan 2017

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Alexander polynomial
twist knots
Virtual knots

Access to Document

10.1142/S0218216517500079

http://digitalcommons.lmu.edu/math_fac/182

Cite this

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title = "The Alexander Polynominal for Virtual Twist Knots",

abstract = "We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial Δ0 (as defined by Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications12 (2003) 987–1000]) of these virtual twist knots. These results are applied to provide evidence for a conjecture that the odd writhe of a virtual knot can be obtained from Δ0 .",

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AB - We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial Δ0 (as defined by Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications12 (2003) 987–1000]) of these virtual twist knots. These results are applied to provide evidence for a conjecture that the odd writhe of a virtual knot can be obtained from Δ0 .

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KW - twist knots

KW - Virtual knots

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DO - 10.1142/S0218216517500079

M3 - Article

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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