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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Rigidity of certain solvable actions on the sphere

Masayuki Asaoka

Geometry & Topology 16 (2012) 1835–1857
Abstract

An analog of the Baumslag–Solitar group BS(1,k) naturally acts on the sphere by conformal transformations. The action is not locally rigid in higher dimensions, but exhibits a weak form of local rigidity. More precisely, any perturbation preserves a smooth conformal structure.

Keywords
group actions, local rigidity
Mathematical Subject Classification 2010
Primary: 37C85
References
Publication
Received: 14 September 2011
Revised: 6 April 2012
Accepted: 13 June 2012
Published: 16 August 2012
Proposed: Benson Farb
Seconded: Leonid Polterovich, Yasha Eliashberg
Authors
Masayuki Asaoka
Department of Mathematics, Kyoto University
Kita-shirakawa Oiwake-cho, Sakyo
Kyoto 606-8502
Japan