Alexander and writhe polynomials for virtual knots

Blake Mellor

Alexander and writhe polynomials for virtual knots

Blake Mellor

Mathematics, Statistics and Data Science

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

Abstract

We give a new interpretation of the Alexander polynomial Δ ₀ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ ₀ determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

Original language	English
Journal	Journal of Knot Theory and its Ramifications
Volume	25
Issue number	8
State	Published - 2016

Disciplines

Geometry and Topology

Cite this

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title = "Alexander and writhe polynomials for virtual knots",

abstract = " We give a new interpretation of the Alexander polynomial Δ 0 for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ 0 determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.",

author = "Blake Mellor",

note = "Mellor, B., 2016: Alexander and writhe polynomials for virtual knots. J. Knot Theory Ramif., 25.8, arXiv:1601.07153.",

year = "2016",

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journal = "Journal of Knot Theory and its Ramifications",

publisher = "World Scientific Publishing",

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AU - Mellor, Blake

N1 - Mellor, B., 2016: Alexander and writhe polynomials for virtual knots. J. Knot Theory Ramif., 25.8, arXiv:1601.07153.

PY - 2016

Y1 - 2016

N2 - We give a new interpretation of the Alexander polynomial Δ 0 for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ 0 determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

AB - We give a new interpretation of the Alexander polynomial Δ 0 for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ 0 determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

UR - https://digitalcommons.lmu.edu/math_fac/32

M3 - Article

VL - 25

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 8

ER -

Alexander and writhe polynomials for virtual knots

Abstract

Disciplines

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