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On medial links and hyperbolic 3-manifolds with large isometry groups

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Abstract

Starting from the regular Platonic solids we construct links, generalizing the Borromean rings, with few components but large finite symmetry groups. We consider the 3-manifolds obtained by equivariant surgeries on these links, most of them hyperbolic, and the quotient orbifolds obtained from these group actions, among them various of the smallest known hyperbolic 3-orbifolds. Also, various of the manifolds obtained by equivariant surgery on these links are maximally symmetric hyperbolic 3-manifolds.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia

    Andrei Vesnin

  2. Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, 34100, Trieste, Italy

    Bruno Zimmermann

Authors
  1. Andrei Vesnin
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  2. Bruno Zimmermann
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Vesnin, A., Zimmermann, B. On medial links and hyperbolic 3-manifolds with large isometry groups. Rend. Circ. Mat. Palermo 50, 347–358 (2001). https://doi.org/10.1007/BF02844991

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  • DOI: https://doi.org/10.1007/BF02844991

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