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Journal of Topology 2008 1(2):461-476; doi:10.1112/jtopol/jtn008
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© 2008 London Mathematical Society

The first homology of the group of equivariant diffeomorphisms and its applications

Kojun Abe

Department of Mathematical Sciences, Shinshu University, Matsumoto 390-8621, Japan kojnabe@shinshu-u.ac.jp

Kazuhiko Fukui

Department of Mathematics, Kyoto Sangyo University Kyoto 603-8555 Japan fukui@cc.kyoto-su.ac.jp


  Abstract

Let V be a representation space of a finite group G. We determine the group structure of the first homology of the equivariant diffeomorphism group of V. Then we can apply it to the calculation of the first homology of the corresponding automorphism groups of smooth orbifolds, compact Hausdorff foliations, codimension one or two compact foliations and the locally free S1-actions on 3-manifolds.

Received November 5, 2007.

2000 Mathematics Subject Classification 58D05, 58D10, 57S05

The first author was partially supported by a Grant-in-Aid for Scientific Research (No.16540058), Japan Society for the Promotion of Science. The second author was partially supported by a Grant-in-Aid for Scientific Research (No.17540098), Japan Society for the Promotion of Science.


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