On the first homology of the group of equivariant Lipschitz homeomorphisms
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Journal of the Mathematical Society of Japan

On the first homology of the group of equivariant Lipschitz homeomorphisms

Kōjun ABE, Kazuhiko FUKUI, and Takeshi MIURA

Source: J. Math. Soc. Japan Volume 58, Number 1 (2006), 1-15.

Abstract

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 $\mathbf{C}^n$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 $L(\mathbf{C},0)$ of Lipschitz homeomorphisms of $\mathbf{C}^n$ fixing the origin.

Primary Subjects: 58D05
Keywords: Lipschitz homeomorphism; commutator; $G$-manifold; continuous moduli

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1145287091
Digital Object Identifier: doi:10.2969/jmsj/1145287091
Mathematical Reviews number (MathSciNet): MR2204563
Zentralblatt MATH identifier: 05015987


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