Automorphic functions with respect to the fundamental group of the complement of the Borromean rings
Vol. 13 (2006), No. 1, Page 1--11.
Matsumoto, Keiji
Automorphic functions with respect to the fundamental group of the complement of the Borromean rings
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Abstract:
We construct automorphic functions on the real 3-dimensional hyperbolic space \H3 with respect to a subgroup B of GL2(Z[i]), which is isomorphic to the fundamental group of the complement of the Borromean rings. We utilize the pull-backs of theta functions on the hermitian symmetric domain \D of type I2,2 under an embedding from \H3 into \D for our construction. These automorphic functions realize the quotient space of the real 3-dimensional upper half space by B as part of an affine algebraic variety in the 6-dimensional Euclidean space.
Keywords: Borromean rings, hyperbolic structures, automorphic functions, theta functions.
Mathematics Subject Classification (2000): 11F55, 14P05, 57M25.
Mathematical Reviews Number: MR2223679
Received: 2005-08-04