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The Hilbert--Smith conjecture for quasiconformal actions
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## The Hilbert--Smith conjecture for quasiconformal actions

### Gaven J. Martin

**Abstract.**
This note announces a proof of the Hilbert--Smith conjecture in the
quasiconformal case: A locally compact group $G$ of quasiconformal
homeomorphisms acting effectively on a Riemannian manifold is a Lie group.
The result established is true in somewhat more generality.

*Copyright 1999 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**05** (1999), pp. 66-70
- Publisher Identifier: S 1079-6762(99)00062-1
- 1991
*Mathematics Subject Classification*. Primary 26A24, 30C60, 53A04, 54F65
*Key words and phrases*.
- Received by the editors November 9, 1998
- Posted on May 28, 1999
- Communicated by Walter Neumann
- Comments (When Available)

**Gaven J. Martin**

Department of Mathematics,
The University of Auckland,
Private Bag 92019,
Auckland,
New Zealand

*E-mail address:* `martin@math.auckland.ac.nz`

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