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The arithmeticity of the figure eight knot orbifolds

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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (1992) The arithmeticity of the figure eight knot orbifolds. In Topology '90. Ohio State University Mathematical Research Institute Publications (1). Walter de Gruyter & Co, Berlin, pp. 169-183. ISBN 3-11-012598-6



Abstract

Continuing their investigation [in Topology '90 (Columbus, OH, 1990), 133–167, de Gruyter, Berlin, 1992;] of the problem of how rarely a hyperbolic orbifold is arithmetic, the authors classify the arithmetic figure eight orbifolds: there are exactly six among the hyperbolic figure eight orbifolds (K,n), n>3. This relies on work by H. Helling, A. C. Kim and J. L. Mennicke ["On Fibonacci groups'', Preprint; per bibl.] and extends a recent result of A. Reid [J. London Math. Soc. (2) 43 (1991), no. 1, 171–184;] that (K,∞) is the only arithmetic knot complement.


Item Type:Book Section
Additional Information:

Papers from the Research Semester in Low-dimensional Topology held at Ohio State University, Columbus, Ohio, February–June 1990.

Uncontrolled Keywords:n-fold cyclic covering of the figure eight knot; figure-eight knot; orbifold; arithmetic
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Topology
ID Code:22139
Deposited On:27 Jun 2013 16:56
Last Modified:12 Dec 2018 15:13

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