Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Equivariant, almost homeomorphic maps between $ S\sp 1$ and $ S\sp 2$

Author: Teruhiko Soma
Journal: Proc. Amer. Math. Soc. 123 (1995), 2915-2920
MSC: Primary 57M50; Secondary 57M60
MathSciNet review: 1277134
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Pi $ be a Fuchsian group isomorphic to a non-trivial, closed surface group, and let $ M = {\mathbb{H}^3}/\Gamma $ be a hyperbolic 3-manifold admitting an isomorphism $ \rho :\Pi \to \Gamma $. Under certain assumptions, Cannon-Thurston and Minsky showed that there exists a $ \rho $-equivariant, surjective, continuous map $ f:S_\infty ^1 \to S_\infty ^2$. In this paper, we prove that there exist zero-measure sets $ {\Lambda ^1}$ in $ S_\infty ^1$ and $ {\Lambda ^2}$ in $ S_\infty ^2$ such that the restriction $ f{\vert _{S_\infty ^1 - {\Lambda ^1}}}:S_\infty ^1 - {\Lambda ^1} \to S_\infty ^2 - {\Lambda ^2}$ is a homeomorphism.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57M50, 57M60

Retrieve articles in all journals with MSC: 57M50, 57M60

Additional Information

Keywords: Hyperbolic 3-manifolds, hyperbolic surfaces, equivariant maps, measured foliations
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society