Geometry & Topology

Intersections in hyperbolic manifolds

Igor Belegradek

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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.

Article information

Geom. Topol., Volume 2, Number 1 (1998), 117-144.

Received: 21 December 1996
Revised: 26 March 1998
Accepted: 17 July 1998
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30F40: Kleinian groups [See also 20H10] 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 57R20: Characteristic classes and numbers
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 32H20 51M10: Hyperbolic and elliptic geometries (general) and generalizations

hyperbolic manifold intersection form representation variety


Belegradek, Igor. Intersections in hyperbolic manifolds. Geom. Topol. 2 (1998), no. 1, 117--144. doi:10.2140/gt.1998.2.117.

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