Volume formulae for fibred cone-manifolds with spherical geometry

A. A. Kolpakov

University of Toronto, Canada

Abstract: We classify cone-manifold structures on a three-dimensional sphere whose singular set consists of fibres of a Seifert fibration. We describe domains of existence of a spherical structure on these cone-manifolds in terms of cone angles, and obtain explicit analytic formulae for their volumes.
Bibliography: 18 titles.

Keywords: spherical geometry, cone-manifold, Seifert fibration.

UDC: 514.135+515.162.8+515.16

MSC: 51M09, 57M25, 57M50

Received: 07.02.2015 and 13.06.2016

DOI: 10.4213/sm8489

 English version: Sbornik: Mathematics, 2016, 207:12, 1693–1708

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