On the geometric boundaries of hyperbolic 4–manifolds

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

References

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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

Volume 4, issue 1 (2000)

Darren D Long and Alan W Reid