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Non compact Euclidean cone 3–manifolds with cone angles less than 2π

Daryl Cooper and Joan Porti

Geometry & Topology Monographs 14 (2008) 173–192

DOI: 10.2140/gtm.2008.14.173

arXiv: 0904.1407
Abstract

We describe some properties of noncompact Euclidean cone manifolds with cone angles less than c less than 2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corollary we classify those with cone angles less than 3π∕2 and those with all cone angles equal to 3π∕2.

Keywords

one-manifolds, soul theorem, Alexandrov spaces
Mathematical Subject Classification

Primary: 57M50

Secondary: 53C23
References
Publication

Received: 31 May 2006
Revised: 19 April 2007
Accepted: 23 April 2007
Published: 29 April 2008
Authors
Daryl Cooper
Department of Mathematics
University of California at Santa Barbara
Santa Barbara CA 93106
USA
Joan Porti
Departament de Matemàtiques
Universitat Autònoma de Barcelona
E-08193 Bellaterra
Spain