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On the geometric boundaries of hyperbolic 4–manifolds

Darren D Long and Alan W Reid

Geometry & Topology 4 (2000) 171–178

arXiv: math.GT/0007197

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
Mathematical Subject Classification 2000
Primary: 57R90
Secondary: 57M50
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Publication
Received: 18 June 2000
Accepted: 19 July 2000
Published: 19 July 2000
Proposed: Walter Neumann
Seconded: Jean-Pierre Otal, Robion Kirby
Authors
Darren D Long
Department of Mathematics
University of California
Santa Barbara
California 93106
USA
Alan W Reid
Department of Mathematics
University of Texas
Austin
Texas 78712
USA