Algebraic & Geometric Topology

Peripheral separability and cusps of arithmetic hyperbolic orbifolds

D B McReynolds

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Abstract

For X=, , or , it is well known that cusp cross-sections of finite volume X–hyperbolic (n+1)–orbifolds are flat n–orbifolds or almost flat orbifolds modelled on the (2n+1)–dimensional Heisenberg group N2n+1 or the (4n+3)–dimensional quaternionic Heisenberg group N4n+3(). We give a necessary and sufficient condition for such manifolds to be diffeomorphic to a cusp cross-section of an arithmetic X–hyperbolic (n+1)–orbifold.

A principal tool in the proof of this classification theorem is a subgroup separability result which may be of independent interest.

Article information

Source
Algebr. Geom. Topol., Volume 4, Number 2 (2004), 721-755.

Dates
Received: 2 April 2004
Accepted: 3 September 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882529

Digital Object Identifier
doi:10.2140/agt.2004.4.721

Mathematical Reviews number (MathSciNet)
MR2100678

Zentralblatt MATH identifier
1058.57012

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20G20: Linear algebraic groups over the reals, the complexes, the quaternions

Keywords
Borel subgroup cusp cross-section hyperbolic space nil manifold subgroup separability.

Citation

McReynolds, D B. Peripheral separability and cusps of arithmetic hyperbolic orbifolds. Algebr. Geom. Topol. 4 (2004), no. 2, 721--755. doi:10.2140/agt.2004.4.721. https://projecteuclid.org/euclid.agt/1513882529


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