Volume 2, issue 1 (1998)

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Intersections in hyperbolic manifolds

Igor Belegradek

Geometry & Topology 2 (1998) 117–144

arXiv: math.GT/9807189

Abstract

We obtain some restrictions on the topology of infinite volume hyperbolic manifolds. In particular, for any n and any closed negatively curved manifold M of dimension 3, only finitely many hyperbolic n–manifolds are total spaces of orientable vector bundles over M.

Keywords
hyperbolic manifold, intersection form, representation variety
Mathematical Subject Classification
Primary: 30F40, 53C23, 57R20
Secondary: 22E40, 32H20, 51M10
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Publication
Received: 21 December 1996
Revised: 26 March 1998
Accepted: 17 July 1998
Published: 20 July 1998
Proposed: David Gabai
Seconded: Walter Neumann, Wolfgang Metzler
Authors
Igor Belegradek
Department of Mathematics and Statistics
McMaster University
1280 Main St West
Hamilton
Ontario
L8S 4K1
Canada