Homological and dynamical study on certain groups of Lipschitz homeomorphisms of the circle

Takashi TSUBOI

doi:10.2969/jmsj/04710001

Takashi TSUBOI

著者情報

ジャーナルフリー

1995 年 47 巻 1 号 p. 1-30

DOI https://doi.org/10.2969/jmsj/04710001

詳細

Published: 1995 Received: 1992/09/01 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) A. Denjoy, Sur les coubes définies par les équations différentielle à la surface du tore, J. Math. Pure Appl., 11 (1932), 333-375.
2) D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math., 22 (1970), 165-173.
3) E. Ghys, Sur l'invariance topologique de la classy de Godbillon-Vey, Ann. Inst. Fourier, 37 (1987), 59-76.
4) E. Ghys, L'invariant de Godbillon-Vey, Seminaire Bourbaki, exposé n° 706,1988/89.
5) E. Ghys et V. Sergiescu, Sur un groupe remarquable de difféomorphismes du cercle, Comment. Math. Helv., 62 (1987), 185/239.
6) C. Godbillon et J. Vey, Un invariant des feuilletages de codimension 1, C. R. Acad. Sci. Paris, 273 (1971), 92-95.
7) P. Greenberg, Classifying spaces for foliations with isolated singularities, Trans. Amer. Math. Soc., 304 (1987), 417-429.
8) M. Herman, Sur la conjugaison differentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49(1979), 5-234.
9) S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publ. Math. IHES, 72 (1990), 5-61.
10) N. Kopell, Commuting diffeomorphisms, Global Analysis, Sympos. Pure Math. Amer. Math. Soc., 14 (1970), 165-184.
11) J. Mather, The vanishing of the homology of certain groups of homeomorphisms, Topology, 10 (1971), 297-298.
12) J. Mather, Commutators of diffeomorphisms I, II and III, Comment. Math. Helv., 49 (1974), 512-528; 50(1975), 33-40; 60 (1985), 122-124.
13) D. Pixton, Nonsmoothable, unstable group actions, Trans. Amer. Math. Soc., 229 (1977), 259-268.
14) T. Tsuboi, On 2-cycles of B Duff (S¹) which are represented by foliated S¹-bundles over T², Ann. Inst. Fourier, 31 (2) (1981), 1-59.
15) T. Tsuboi, On the homology of classifying spaces for foliated products, Adv. Stud. Pure Math., 5 Foliations (1985), 37-120.
16) T. Tsuboi, Foliations and homology of the group of diffeomorphisms, Sûgaku, 34 (1984), 320-343; English traslation, Sugaku Expositions, 3 (1990), 145-181.
17) T. Tsuboi, On the foliated products of class C¹, Ann. of Math., 130 (1989), 227-271.
18) T. Tsuboi, On the Hurder-Katok extension of the Godbillon-Vey invariant, J. Fac. Sci. Univ. Tokyo Sec. lA Math., 37 (1990), 255-262.
19) T. Tsuboi, Area functionals and Godbillon-Vey cocycles, Ann. Inst. Fourier, 42 (1992), 421-447.
20) T. Tsuboi, Small commutators in piecewise linear homeomorphisms of the real line, to appear in Topology.
21) T. Tsuboi, The Godbillon-Vey invariant and the foliated cobordism group, Proc. Japan Acad. Ser. A Math. Sci., 68 (1992), 85-90.

Right : [1] A. Denjoy, Sur les coubes définies par les équations différentielle à la surface du tore, J. Math. Pure Appl., 11 (1932), 333-375.
[2] D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math., 22 (1970), 165-173.
[3] E. Ghys, Sur l'invariance topologique de la classy de Godbillon-Vey, Ann. Inst. Fourier, 37 (1987), 59-76.
[4] E. Ghys, L'invariant de Godbillon-Vey, Seminaire Bourbaki, exposé n° 706,1988/89.
[5] E. Ghys et V. Sergiescu, Sur un groupe remarquable de difféomorphismes du cercle, Comment. Math. Helv., 62 (1987), 185/239.
[6] C. Godbillon et J. Vey, Un invariant des feuilletages de codimension 1, C. R. Acad. Sci. Paris, 273 (1971), 92-95.
[7] P. Greenberg, Classifying spaces for foliations with isolated singularities, Trans. Amer. Math. Soc., 304 (1987), 417-429.
[8] M. Herman, Sur la conjugaison differentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49(1979), 5-234.
[9] S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publ. Math. IHES, 72 (1990), 5-61.
[10] N. Kopell, Commuting diffeomorphisms, Global Analysis, Sympos. Pure Math. Amer. Math. Soc., 14 (1970), 165-184.
[11] J. Mather, The vanishing of the homology of certain groups of homeomorphisms, Topology, 10 (1971), 297-298.
[12] J. Mather, Commutators of diffeomorphisms I, II and III, Comment. Math. Helv., 49 (1974), 512-528; 50(1975), 33-40; 60 (1985), 122-124.
[13] D. Pixton, Nonsmoothable, unstable group actions, Trans. Amer. Math. Soc., 229 (1977), 259-268.
[14] T. Tsuboi, On 2-cycles of B Duff (S¹) which are represented by foliated S¹-bundles over T², Ann. Inst. Fourier, 31 (2) (1981), 1-59.
[15] T. Tsuboi, On the homology of classifying spaces for foliated products, Adv. Stud. Pure Math., 5 Foliations (1985), 37-120.
[16] T. Tsuboi, Foliations and homology of the group of diffeomorphisms, Sûgaku, 34 (1984), 320-343; English traslation, Sugaku Expositions, 3 (1990), 145-181.
[17] T. Tsuboi, On the foliated products of class C¹, Ann. of Math., 130 (1989), 227-271.
[18] T. Tsuboi, On the Hurder-Katok extension of the Godbillon-Vey invariant, J. Fac. Sci. Univ. Tokyo Sec. lA Math., 37 (1990), 255-262.
[19] T. Tsuboi, Area functionals and Godbillon-Vey cocycles, Ann. Inst. Fourier, 42 (1992), 421-447.
[20] T. Tsuboi, Small commutators in piecewise linear homeomorphisms of the real line, to appear in Topology.
[21] T. Tsuboi, The Godbillon-Vey invariant and the foliated cobordism group, Proc. Japan Acad. Ser. A Math. Sci., 68 (1992), 85-90.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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