On the first homology of the group of equivariant Lipschitz homeomorphisms

DOI Web Site 参考文献14件
  • Abe Kojun
    Department of Mathematical Sciences, Shinshu University
  • Fukui Kazuhiko
    Department of Mathematics, Kyoto Sangyo University
  • Miura Takeshi
    Department of Basic Technology, Applied Mathematics and Physics, Yamagata University

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We study the structure of the group of equivariant Lipschitz homeomorphisms of a smooth G-manifold M which are isotopic to the identity through equivariant Lipschitz homeomorphisms with compact support. First we show that the group is perfect when M is a smooth free G-manifold. Secondly in the case of Cn with the canonical U(n)-action, we show that the first homology group admits continuous moduli. Thirdly we apply the result to the case of the group L(C, 0) of Lipschitz homeomorphisms of C fixing the origin.

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