# On the first homology of automorphism groups of manifolds with geometric structures

Open Mathematics (2005)

- Volume: 3, Issue: 3, page 516-528
- ISSN: 2391-5455

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topKōjun Abe, and Kazuhiko Fukui. "On the first homology of automorphism groups of manifolds with geometric structures." Open Mathematics 3.3 (2005): 516-528. <http://eudml.org/doc/268694>.

@article{KōjunAbe2005,

abstract = {Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.},

author = {Kōjun Abe, Kazuhiko Fukui},

journal = {Open Mathematics},

keywords = {47S05; 58D05; 58H10},

language = {eng},

number = {3},

pages = {516-528},

title = {On the first homology of automorphism groups of manifolds with geometric structures},

url = {http://eudml.org/doc/268694},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Kōjun Abe

AU - Kazuhiko Fukui

TI - On the first homology of automorphism groups of manifolds with geometric structures

JO - Open Mathematics

PY - 2005

VL - 3

IS - 3

SP - 516

EP - 528

AB - Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.

LA - eng

KW - 47S05; 58D05; 58H10

UR - http://eudml.org/doc/268694

ER -

## References

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