Equivariant, almost homeomorphic maps between and

Author:
Teruhiko Soma

Journal:
Proc. Amer. Math. Soc. **123** (1995), 2915-2920

MSC:
Primary 57M50; Secondary 57M60

DOI:
https://doi.org/10.1090/S0002-9939-1995-1277134-3

MathSciNet review:
1277134

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Abstract: Let be a Fuchsian group isomorphic to a non-trivial, closed surface group, and let be a hyperbolic 3-manifold admitting an isomorphism . Under certain assumptions, Cannon-Thurston and Minsky showed that there exists a -equivariant, surjective, continuous map . In this paper, we prove that there exist zero-measure sets in and in such that the restriction is a homeomorphism.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1277134-3

Keywords:
Hyperbolic 3-manifolds,
hyperbolic surfaces,
equivariant maps,
measured foliations

Article copyright:
© Copyright 1995
American Mathematical Society