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The groups of quasiconformal homeomorphisms on Riemann surfaces

Author: Tatsuhiko Yagasaki
Journal: Proc. Amer. Math. Soc. 127 (1999), 2727-2734
MSC (1991): Primary 30C62, 57N05, 57N20
Published electronically: April 15, 1999
MathSciNet review: 1600094
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Abstract: Suppose $M$ is a connected Riemann surface. Let ${\mathcal H}(M)$ denote the homeomorphism group of $M$ with the compact-open topology, and ${\mathcal H}^{\mathrm{QC}}(M)$ denote the subgroup of quasiconformal mappings of $M$ onto itself, and let ${\mathcal H}(M)_0$ and ${\mathcal H}^{\mathrm{QC}}(M)_0$ denote the identity components of ${\mathcal H}(M)$ and ${\mathcal H}^{\mathrm{QC}}(M)$ respectively. In this paper we show that the pair $({\mathcal H}(M)_0, {\mathcal H}^{\mathrm{QC}}(M)_0)$ is an $(s, \Sigma)$-manifold, and determine their topological types.

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Additional Information

Tatsuhiko Yagasaki
Affiliation: Department of Mathematics, Kyoto Institute of Technology, Matsugasaki, Sakyoku, Kyoto 606, Japan

Keywords: Quasiconformal mappings, Riemann surfaces, homeomorphisms, infinite-dimensional manifolds
Received by editor(s): March 20, 1997
Received by editor(s) in revised form: November 28, 1997
Published electronically: April 15, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society

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