2023-11-29T19:48:35Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/586272023-08-25T14:34:34Zcom_20.500.14352_14col_20.500.14352_15
Hilden, Hugh Michael
Lozano Imízcoz, María Teresa
Montesinos Amilibia, José María
2023-06-20T18:47:30Z
2023-06-20T18:47:30Z
1993
0218-2165
10.1142/S021821659300009X
https://hdl.handle.net/20.500.14352/58627
http://www.worldscientific.com/doi/abs/10.1142/S021821659300009X
http://www.worldscientific.com/
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.
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Universal 2-bridge knot and link orbifolds
journal article