On character varieties of two-bridge knot groups

Melissa L. MacAsieb, Kathleen L. Petersen, Ronald M. Van Luijk

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We find explicit models for the PSL2()- and SL2()-character varieties of the fundamental groups of complements in 3 of an infinite family of two-bridge knots that contains the twist knots. We compute the genus of the components of these character varieties, and deduce upper bounds on the degree of the associated trace fields. We also show that these knot complements are fibered if and only if they are commensurable to a fibered knot complement in a /2-homology sphere, resolving a conjecture of Hoste and Shanahan. 2011 London Mathematical Society2011

Original languageEnglish (US)
Pages (from-to)473-507
Number of pages35
JournalProceedings of the London Mathematical Society
Volume103
Issue number3
DOIs
StatePublished - Sep 2011
Externally publishedYes

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