메뉴 건너뛰기




Volumn 103, Issue 1, 2004, Pages 205-223

A vanishing theorem for the tangential de Rham cohomology of a foliation with amenable fundamental groupoid

Author keywords

Amenable; Cohomology; Foliation; Fundamental groupoid; Nonpositive curvature; Rank

Indexed keywords


EID: 3843116692     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:GEOM.0000013865.22152.0c     Document Type: Article
Times cited : (4)

References (22)
  • 3
    • 0004145531 scopus 로고    scopus 로고
    • Enseign. Math., Geneva, With a foreword by Georges Skandalis and Appendix B by E. Germain
    • Anatharaman-Delaroche, C. and Renault, J.: Amenable groupoids, Enseign. Math., Geneva, 2000. With a foreword by Georges Skandalis and Appendix B by E. Germain.
    • (2000) Amenable Groupoids
    • Anatharaman-Delaroche, C.1    Renault, J.2
  • 4
    • 0001019149 scopus 로고
    • Stable real homology of arithmetic groups
    • Borel, A.: Stable real homology of arithmetic groups, Ann. Sci. Ecole Norm. Super. 7(4), (1974), 235-272.
    • (1974) Ann. Sci. Ecole Norm. Super. , vol.7 , Issue.4 , pp. 235-272
    • Borel, A.1
  • 5
    • 0000838113 scopus 로고
    • An amenable equivalence relation is generated by a single transformation
    • Connes, A., Feldman, J. and Weiss, B.: An amenable equivalence relation is generated by a single transformation, Ergodic Theory Dynam. Systems 1 (1982), 431-450.
    • (1982) Ergodic Theory Dynam. Systems , vol.1 , pp. 431-450
    • Connes, A.1    Feldman, J.2    Weiss, B.3
  • 6
    • 84968495052 scopus 로고
    • Ergodic equivalence relations, cohomology, and von Neumann algebras, I, II
    • Feldman, J. and Moore, C. C.: Ergodic equivalence relations, cohomology, and von Neumann algebras. I, II, Trans. Amer. Math. Soc. 234 (1977), 289-324, 325-359.
    • (1977) Trans. Amer. Math. Soc. , vol.234 , pp. 289-324
    • Feldman, J.1    Moore, C.C.2
  • 7
    • 0003912330 scopus 로고
    • Cambridge Stud. Adv. Math. 27, Cambridge University Press, Cambridge
    • Fröhlich, A. and Taylor, M.: Algebraic Number Theory, Cambridge Stud. Adv. Math. 27, Cambridge University Press, Cambridge, 1993.
    • (1993) Algebraic Number Theory
    • Fröhlich, A.1    Taylor, M.2
  • 8
    • 0002344449 scopus 로고
    • Inst. Hautes Études Sci. Publ. Math
    • Gromov, M.: Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1983), 5-99.
    • (1983) Volume and Bounded Cohomology , vol.56 , pp. 5-99
    • Gromov, M.1
  • 10
    • 0003408652 scopus 로고
    • Springer-Verlag, New York. With appendices by S. Hurder, C. C. Moore, C. Schochet and R. J. Zimmer
    • Moore, C. C. and Schochet, C.: Global Analysis on Foliated Spaces, Springer-Verlag, New York, 1988. With appendices by S. Hurder, C. C. Moore, C. Schochet and R. J. Zimmer.
    • (1988) Global Analysis on Foliated Spaces
    • Moore, C.C.1    Schochet, C.2
  • 12
    • 0011970883 scopus 로고
    • Amer. Math. Soc., Providence, RI. Translated from the Japanese original by the author
    • Sakai, T.: Riemannian Geometry. Amer. Math. Soc., Providence, RI, 1996. Translated from the 1992 Japanese original by the author.
    • (1992) Riemannian Geometry
    • Sakai, T.1
  • 13
    • 84974336812 scopus 로고
    • An example of an amenable action from geometry
    • Spatzier, R. J.: An example of an amenable action from geometry, Ergodic Theory Dynam. Systems 7(2) (1987), 289-293.
    • (1987) Ergodic Theory Dynam. Systems , vol.7 , Issue.2 , pp. 289-293
    • Spatzier, R.J.1
  • 14
    • 0000485129 scopus 로고
    • Fundamental groups of negatively curved manifolds and actions of semisimple groups
    • Spatzier, R. J. and Zimmer, R. J.: Fundamental groups of negatively curved manifolds and actions of semisimple groups, Topology 30(4) (1991), 591-601.
    • (1991) Topology , vol.30 , Issue.4 , pp. 591-601
    • Spatzier, R.J.1    Zimmer, R.J.2
  • 17
    • 26444562048 scopus 로고    scopus 로고
    • in preparation, version of October 23rd
    • Witte, D.: Introduction to arithmetic groups. in preparation, version of October 23rd, 2001 available at http://www.math.okstate.edu/~dwitte/ LectureNotes.shtml#Arithmetic Groups.
    • (2001) Introduction to Arithmetic Groups
    • Witte, D.1
  • 18
    • 0040708153 scopus 로고
    • Hyperfinite factors and amenable ergodic actions
    • Zimmer, R. J.: Hyperfinite factors and amenable ergodic actions, Invent. Math. 41(1) (1977), 23-31.
    • (1977) Invent. Math. , vol.41 , Issue.1 , pp. 23-31
    • Zimmer, R.J.1
  • 19
    • 0001559020 scopus 로고
    • Amenable ergodic group actions and an application to Poisson boundaries of random walks
    • Zimmer, R. J.: Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal. 27(3) (1978), 350-372.
    • (1978) J. Funct. Anal. , vol.27 , Issue.3 , pp. 350-372
    • Zimmer, R.J.1
  • 20
    • 0010077011 scopus 로고
    • Curvature of leaves in amenable foliations
    • Zimmer, R. J.: Curvature of leaves in amenable foliations, Amer. J. Math. 105 (1983), 1011-1022.
    • (1983) Amer. J. Math. , vol.105 , pp. 1011-1022
    • Zimmer, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.