Skip to main content
SpringerLink
Log in

Holonomy Groups of Solvable Lie Foliations

  • Conference paper
Integrable Systems and Foliations

Part of the book series: Progress in Mathematics ((PM,volume 145))

Abstract

Following C. Ehresmann, to every foliated manifold one associates a pseudogroup of transformations that represents the transverse structure of the foliation. Conversely, every pseudogroup comes from a foliated manifold.

Dedicated — with friendly admiration — to Pierre Molino for his sixtieth birthday.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Bieri, Gruppen mit Poincaré-Dualitàt, Comment. Math. Helv. 47 (1972), 373–396.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Bieri, The geometric invariants of a group — a survey with emphasis on the homotopical approach, Proc. Conf. on Geometric Methods in Group Theory, Sussex, 1991.

    Google Scholar 

  3. R. Bieri, R. Strebel: Valuations and Finitely Presented Metabelian Groups, Proc. London Math. Soc. 41 (3) (1980), 439–464.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Bieri, R. Strebel: A geometric invariant for nilpotent-by-abelian-by-finite groups, Journal of Pure and Appl. Algebra 25 (1982), 1–20.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Bieri, W. D. Neumann, R. Strebel, A geometric invariant of discrete groups, Invent. Math. 90 (1987), 451–477.

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. Carrière, Sur la croissance des feuilletages de Lie, Pub. IRMA, Lille VI (3) (1984).

    Google Scholar 

  7. V. Cavalier, pseudogroupes complexes quasi parallélisables de dimension 1 Ann. Inst. Fourier, Grenoble 44 (5) (1994), 1–27.

    MathSciNet  Google Scholar 

  8. C. Ehresmann, Sur les espaces localement homogènes, L’enseignement Mathématique 5–6 (1936), 317–333.

    Google Scholar 

  9. C. Ehresmann, Structures locales, Annali di Mat. (1954), 133–142.

    Google Scholar 

  10. E. Fédida, Feuilletages de Lie, feuilletages du plan, thèse, Strasbourg (1973),L.N.M. 352, 183–195.

    Google Scholar 

  11. E. Ghys, Groupes d’holonomie des feuilletages de Lie, Indag. Math. 47 (2) (1985).

    Google Scholar 

  12. [Ha1]A. Haefliger, Groupoïde d’holonomie et classifiants, in: Structures transverses des feuilletages, Toulouse 1982, Astérisque 116 (1984), 70–97.

    Google Scholar 

  13. A. Haefliger: pseudogroups of Local Isometries. in Proc. Vth Coll. in Diff. Geom., ed. L. A. Cordero, Research Notes in Math. 131, Pitman (1985), 174–197.

    Google Scholar 

  14. R. Hermann: A sufficient condition that a mapping of Riemannian manifolds be a fiber bundle, Proc. AMS 11 (1960), 236–242.

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Meigniez, Actions de groupes sur la droite et feuilletages de codimension 1, thèse, Univ. Claude Bernard-Lyon I (1988).

    Google Scholar 

  16. G. Meigniez, Sous-groupes de génération compacte des groupes de Lie résolubles, preprint Math. Univ. Paris 7, 33 (1992).

    Google Scholar 

  17. G. Meigniez, Feuilletages de Lie résolubles, Annales de la faculté des sciences de Toulouse IV (4) (1995), 1–17.

    Google Scholar 

  18. S. Matsumoto, N. Tsuchiya: Lie Affine Foliations on 4-Manifolds, preprint.

    Google Scholar 

  19. B. L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1) (1959), 119–132.

    Article  MathSciNet  MATH  Google Scholar 

  20. D. Tischler, On fibering certain foliated manifolds over S 1, Topology 9 (1970), 153–154.

    Article  MathSciNet  MATH  Google Scholar 

  21. O. Veblen, J.H.C. Whitehead, A set of axioms for Differential Geometry, Proc. Nat. Acad. Sci. 17 (1931), 551–561.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathématiques, Institut Girard Desargues, Université Claude Bernard-Lyon 1, 43, boulevard du 11 novembre 1918, 69622, Villeurbanne Cedex, France

    Gaêl Meigniez

Authors
  1. Gaêl Meigniez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Départment de Mathématiques Case 51, Université Montpellier II, France

    Claude Albert , Robert Brouzet  & Jean Paul Dufour ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Birkhäuser Boston

About this paper

Cite this paper

Meigniez, G. (1997). Holonomy Groups of Solvable Lie Foliations. In: Albert, C., Brouzet, R., Dufour, J.P. (eds) Integrable Systems and Foliations. Progress in Mathematics, vol 145. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4134-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4134-8_7

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8668-4

  • Online ISBN: 978-1-4612-4134-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation