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Hyperbolic Structure on "link" complements in S4
by
Dubravko Ivanšić
The George Washington University
It is well known that many link complements in S3 support a hyperbolic structure. Can the same be said for one dimension higher, i.e. inside S4?
Previous work of this author has determined that if a finite-volume noncompact hyperbolic 4-manifold M is to be considered a complement of a codimension-2 submanifold A inside a closed 4-manifold N, that is, if M=N-A, then A is necessarily a union of flat 2-manifolds, thus, tori and Klein Bottles.
The most interesting situation seems to be when N=S4. We show that two nonorientable examples from a long list of hyperbolic 4-manifolds constructed by Ratcliffe and Tschantz have double covers that are homeomorphic to complements of several tori inside S4.
http://gwis2.circ.gwu.edu/~divansic
Date received: February 8, 2000
Copyright © 2000 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caea-24.