PALINDROME PRESENTATIONS OF RATIONAL KNOTS-Reference-Cited by-同舟云学术

PALINDROME PRESENTATIONS OF RATIONAL KNOTS

Published:2009-03 Issue:03 Volume:18 Page:343-361
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

CAVICCHIOLI ALBERTO¹,REPOVŠ DUŠAN²,SPAGGIARI FULVIA¹

Affiliation:

1. Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy

2. Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana 1001, Slovenia

Abstract

We give explicit palindrome presentations of the groups of rational knots, i.e. presentations with relators which read the same forwards and backwards. This answers a question posed by Hilden, Tejada and Toro in 2002. Using such presentations we obtain simple alternative proofs of some classical results concerning the Alexander polynomial of all rational knots and the character variety of certain rational knots. Finally, we derive a new recursive description of the SL(2, ℂ) character variety of twist knots.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216509006963

Reference27 articles.

1. ON BRANCHED COVERINGS OF LENS SPACES

2. SU(2)-representation spaces for two-bridge knot groups

3. TOPOLOGICAL PROPERTIES OF CYCLICALLY PRESENTED GROUPS

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