The orientation-preserving diffeomorphism group of \mathbbS² deforms to SO(3) smoothly

2009/12/31 by Jiayong Li, Jordan Alan Watts · 2 citations
Mathematics · #Algebra over a field #Analytic and geometric function theory #Construct (python library) #Deformation (meteorology) #Diffeomorphism #Geometric and Algebraic Topology #Group (periodic table) #Mathematical Dynamics and Fractals #Surface (topology) #math.DG #math.SG

paper · pdf · doi:10.1007/s00031-011-9130-0

published in Transformation Groups 16(2), 537-553 (Birkhäuser) · 16 pages

arxiv created 2010/04/01 · openalex publication_date 2011/03/23 · arxiv updated 2011/07/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Smale proved that the orientation-preserving diffeomorphism group of S² has a continuous strong deformation retraction to SO(3). In this paper, we construct such a strong deformation retraction which is diffeologically smooth.

Citations

• Smooth functions invariant under the action of a compact lie group
• Diffeomorphisms of the 2-sphere