TY - JOUR
T1 - On character varieties of two-bridge knot groups
AU - MacAsieb, Melissa L.
AU - Petersen, Kathleen L.
AU - Van Luijk, Ronald M.
PY - 2011/9
Y1 - 2011/9
N2 - 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
AB - 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
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U2 - 10.1112/plms/pdr003
DO - 10.1112/plms/pdr003
M3 - Article
AN - SCOPUS:80052364111
SN - 0024-6115
VL - 103
SP - 473
EP - 507
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
IS - 3
ER -