RT Journal Article
T1 Universal 2-bridge knot and link orbifolds
A1 Hilden, Hugh Michael
A1 Lozano Imízcoz, María Teresa
A1 Montesinos Amilibia, José María
AB Let (L,n) be the orbifold with singular set a nontoroidal 2-bridge knot or link L in S3, with cyclic isotropy group of order n. The authors show that the orbifold fundamental group Γ=π1(L,12n) is universal: Γ is isomorphic to a discrete group of isometries of the hyperbolic 3-space H3, and any closed oriented 3-manifold is homeomorphic to H3/G for some subgroup of finite index G of Γ. They show that the Borromean link in S3 is a sublink of the preimage of the singular set of a branched cover over L, with branching indices dividing 12. Since they had proved in an earlier paper that the orbifold with singular set the Borromean link and cyclic isotropy groups of orders 4,4,4 is universal, the result follows. In particular, if L is the figure eight knot, then π1(L,12) is both universal and arithmetic.
PB World Scientific PublCo
SN 0218-2165
YR 1993
FD 1993
LK https://hdl.handle.net/20.500.14352/58627
UL https://hdl.handle.net/20.500.14352/58627
DS Docta Complutense
RD 2 dic 2023