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Totally geodesic surfaces in hyperbolic 3-manifolds

Published online by Cambridge University Press:  20 January 2009

Alan W. Reid
Alan W. Reid
Affiliation:
Department of MathematicsThe Ohio State University231 West 18th AvenueColumbus, OH 43210, USA
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Abstract

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In this paper we investigate totally geodesic surfaces in hyperbolic 3-manifolds. In particular we show that if M is a compact arithmetic hyperbolic 3-manifold containing an immersion of a totally geodesic surface then it contains infinitely many commensurability classes of such surfaces. In addition we show for these M that the Chern-Simons invariant is rational.

We also show, that unlike the figure-eight knot complement in S3, many knot complements in S3 do not contain an immersion of a closed totally geodesic surface.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 1 , February 1991 , pp. 77 - 88
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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