Simplicity of the group of compactly supported area preserving homeomorphisms of the open disc and fragmentation of symplectic diffeomorphisms

2009/01/16 by Frédéric Le Roux, Roux, Frédéric Le
Mathematics · #28D15. #37E30 #57S99 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.0901.2428

openalex publication_date 2009/01/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In 1980, Albert Fathi asked whether the group of area-preserving homeomorphisms of the 2-disc that are the identity near the boundary is a simple group. In this paper, we show that the simplicity of this group is equivalent to the following fragmentation property in the group of compactly supported, area preserving diffeomorphisms of the plane: there exists a constant m such that every element supported on a disc D is the product of at most m elements supported on topological discs whose area are half the area of D.

Related

• Proof of the simplicity conjecture
• The sharp C⁰-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces
• Example of an unbounded diffeomorphism group
• Topological extension of Calabi invariants and non-simpleness of the area preserving homeomorphism group of the disc
• Diffeomorphisms of discs