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Spherical structures on torus knots and links

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Abstract

We study two infinite families of cone manifolds endowed with a spherical metric. The singular set of the first of them is the torus knot t(2n + 1, 2) and the singular set of the second is the two-component link t(2n, 2). We find the domains of sphericity of these cone manifolds in terms of cone angles and obtain analytic formulas for their volumes.

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Correspondence to A. A. Kolpakov.

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To Academician Yuriĭ Grigor’evich Reshetnyak on his 80th birthday.

Original Russian Text Copyright © 2009 Kolpakov A. A. and Mednykh A. D.

The authors were supported by the Russian Foundation for Basic Research (Grant 09-01-00255) and the State Maintenance Program for the Leading Scientific Schools and Junior Scientists of the Russian Federation (Grant NSh-5682.2008.1).

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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 5, pp. 1083–1096, September–October, 2009.

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Kolpakov, A.A., Mednykh, A.D. Spherical structures on torus knots and links. Sib Math J 50, 856–866 (2009). https://doi.org/10.1007/s11202-009-0096-2

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  • DOI: https://doi.org/10.1007/s11202-009-0096-2

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