An Alexander-type invariant for doodles-Reference-Cited by-同舟云学术

An Alexander-type invariant for doodles

Published:2022-11 Issue:13 Volume:31 Page:
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Cisneros Bruno¹,Flores Marcelo²,Juyumaya Jesús²,Roque-Márquez Christopher³⁴

Affiliation:

1. Instituto de Matemáticas, UNAM, León No. 2, Altos, Oaxaca de Juárez 68000, México

2. Instituto de Matemáticas, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso 2340000, Chile

3. Centro de Ciencias Matemáticas, UNAM, Antigua Carretera a Pátzcuaro No. 8701, Morelia 58089, México

4. Universidad La Salle Morelia, Av. Universidad 500, Tarímbaro 58880, México

Abstract

We construct an Alexander-type invariant for oriented doodles from a deformation of the Tits representation of the twin group and from the Chebyshev polynomials of the second kind. Like the Alexander polynomial, our invariant vanishes on unlinked doodles with more than one component. We also include values of our invariant on several doodles.

Funder

FONDECYT

CONACYT Ciencia de Frontera 2019

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216522500900

Reference29 articles.

1. Doodle groups

2. Инварианты Васильева классифицируют плоские кривые и наборы кривых без тройных пересечений

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