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Rigidity of certain solvable actions on the sphere

Masayuki Asaoka
Geometry & Topology 16 (2012) 1835–1857
DOI: 10.2140/gt.2012.16.1835
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