Geometry & Topology, Vol. 4 (2000) Paper no. 5, pages 171--178.

On the geometric boundaries of hyperbolic 4-manifolds

DD Long and AW Reid

Abstract. We provide, for hyperbolic and flat 3-manifolds, obstructions to bounding hyperbolic 4-manifolds, thus resolving in the negative a question of Farrell and Zdravkovska.

Keywords. Hyperbolic 3-manifold, flat manifold, totally geodesic, eta-invariant

AMS subject classification. Primary: 57R90. Secondary: 57M50.

DOI: 10.2140/gt.2000.4.171

E-print: arXiv:math.GT/0007197

Submitted to GT on 18 June 2000. Paper accepted 19 July 2000. Paper published 19 July 2000.

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DD Long AW Reid
Department of Mathematics, University of California
Santa Barbara, CA 93106, USA

Department of Mathematics, University of Texas
Austin, TX 78712, USA

Email: long@math.ucsb.edu, areid@math.utexas.edu

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