Geometry & Topology, Vol. 2 (1998) Paper no. 7, pages 117--144.

Intersections in hyperbolic manifolds

Igor Belegradek

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 greater than 2, only finitely many hyperbolic n-manifolds are total spaces of orientable vector bundles over M.

Keywords. Hyperbolic manifold, intersection form, representation variety

AMS subject classification. Primary: 30F40, 53C23, 57R20. Secondary: 22E40, 32H20, 51M10.

DOI: 10.2140/gt.1998.2.117

E-print: arXiv:math.GT/9807189

Submitted to GT on 21 December 1996. (Revised 26 March 1998.) Paper accepted 17 July 1998. Paper published 20 July 1998.

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Igor Belegradek
Department of Mathematics and Statistics
McMaster University
1280 Main St West
Hamilton, ON L8S 4K1

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