The Alexander Polynominal for Virtual Twist Knots

Authors

Isaac Benioff
Blake Mellor, Loyola Marymount UniversityFollow

Document Type

Article - pre-print

Publication Date

2017

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 .

Comments

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Original Publication Citation

Benioff, Isaac, and Blake Mellor. “The Alexander Polynomial for Virtual Twist Knots.” Journal of Knot Theory and Its Ramifications 26, no. 01 (January 2017): 1750007. https://doi.org/10.1142/S0218216517500079.

Digital Commons @ LMU & LLS Citation

Benioff, Isaac and Mellor, Blake, "The Alexander Polynominal for Virtual Twist Knots" (2017). Mathematics, Statistics and Data Science Faculty Works. 182.
https://digitalcommons.lmu.edu/math_fac/182