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Book Information:
Authors:
I. Moerdijk and
J. Mrcun
Title:
Introduction to foliations and Lie groupoids
Additional book information:
Cambridge University Press,
Cambridge, UK,
2003,
x+173 pp.,
ISBN 0-521-83197-0,
£30.00
Rui Almeida and Pierre Molino, Suites d’Atiyah et feuilletages transversalement complets, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 1, 13–15 (French, with English summary). MR 778785
Alain Connes, Sur la théorie non commutative de l’intégration, Algèbres d’opérateurs (Sém., Les Plans-sur-Bex, 1978) Lecture Notes in Math., vol. 725, Springer, Berlin, 1979, pp. 19–143 (French). MR 548112
Alain Connes, Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994. MR 1303779
4. C. Ehresmann, Structures Feuilletées, Proc. 5th Canadian Math. Congress, Univ. of Toronto Press 1963, 1961, pp. 109-172.
5. E. Fedida, Feulletages du plan, feuilletages de Lie, Thesis, Strasbourg (1983).
André Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 16 (1962), 367–397 (French). MR 189060
A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), 183–194 (French). MR 263104, DOI 10.1016/0040-9383(70)90040-6
Pierre Molino, Étude des feuilletages transversalement complets et applications, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 3, 289–307 (French). MR 458446
Pierre Molino, Riemannian foliations, Progress in Mathematics, vol. 73, Birkhäuser Boston, Inc., Boston, MA, 1988. Translated from the French by Grant Cairns; With appendices by Cairns, Y. Carrière, É. Ghys, E. Salem and V. Sergiescu. MR 932463, DOI 10.1007/978-1-4684-8670-4
I. Moerdijk and J. Mrčun, Introduction to foliations and Lie groupoids, Cambridge Studies in Advanced Mathematics, vol. 91, Cambridge University Press, Cambridge, 2003. MR 2012261, DOI 10.1017/CBO9780511615450
Janez Mrčun, An extension of the Reeb stability theorem, Topology Appl. 70 (1996), no. 1, 25–55. MR 1387824, DOI 10.1016/0166-8641(94)00111-1
S. P. Novikov, The topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248–278 (Russian). MR 0200938
Valentin Poénaru, Homotopy theory and differentiable singularities, Manifolds–Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 106–132. MR 0285026
Jean Pradines, Théorie de Lie pour les groupoïdes différentiables. Calcul différenetiel dans la catégorie des groupoïdes infinitésimaux, C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A245–A248 (French). MR 216409
Georges Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Publ. Inst. Math. Univ. Strasbourg, vol. 11, Hermann & Cie, Paris, 1952 (French). MR 0055692
Bruce L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119–132. MR 107279, DOI 10.2307/1970097
V. V. Solodov, Components of topological foliations, Mat. Sb. (N.S.) 119(161) (1982), no. 3, 340–354, 447 (Russian). MR 678831
William P. Thurston, A generalization of the Reeb stability theorem, Topology 13 (1974), 347–352. MR 356087, DOI 10.1016/0040-9383(74)90025-1
William Thurston, The theory of foliations of codimension greater than one, Comment. Math. Helv. 49 (1974), 214–231. MR 370619, DOI 10.1007/BF02566730
W. P. Thurston, Existence of codimension-one foliations, Ann. of Math. (2) 104 (1976), no. 2, 249–268. MR 425985, DOI 10.2307/1971047
H. E. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom. 1 (1983), no. 3, 51–75. MR 739904, DOI 10.1007/BF02329732
H. E. Winkelnkemper, The number of ends of the universal leaf of a Riemannian foliation, Differential geometry (College Park, Md., 1981/1982) Progr. Math., vol. 32, Birkhäuser, Boston, Mass., 1983, pp. 247–254. MR 702537
- 1.
- R. Almeida and P. Molino, Suites d'Atiyah et feuilletages transversalement complets, C. R. Acad. Sci. Paris 300 (1985), 13-15. MR 0778785
- 2.
- A. Connes, Sur la théorie non commutative de l'intégration, Algèbres d'opérateurs (Sém., Les Plans-sur-Bex, 1978), Springer-Verlag, Berlin, 1979, pp. 19-143. MR 0548112
- 3.
- -, Noncommutative Geometry, Academic Press Inc., San Diego, CA, 1994. MR 1303779
- 4.
- C. Ehresmann, Structures Feuilletées, Proc. 5th Canadian Math. Congress, Univ. of Toronto Press 1963, 1961, pp. 109-172.
- 5.
- E. Fedida, Feulletages du plan, feuilletages de Lie, Thesis, Strasbourg (1983).
- 6.
- A. Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa 16 (1962), 367-397. MR 0189060
- 7.
- -, Feuilletages sur les variétés ouvertes, Topology 9 (1970), 183-194. MR 0263104
- 8.
- P. Molino, Etude des feuilletages transversalement complets et applications, Ann. Scient. Ec. Norm. Sup. 10 (1977), 289-307. MR 0458446
- 9.
- -, Riemannian Foliations, Birkhaüser, Boston, Massachusetts, 1988, Translated from the French by G. Cairns, with appendices by Cairns, Y. Carrière, É. Ghys, E. Salem and V. Sergiescu. MR 0932463 (89b:53054)
- 10.
- I. Moerdijk and J. Mrcun, Introduction to Foliations and Lie Groupoids, Cambridge University Press, Cambridge, UK, 2003. MR 2012261
- 11.
- J. Mrcun, An extension of the Reeb stability theorem, Top. and Appl 70 (1996), 25-55. MR 1387824 (97j:57035)
- 12.
- S. P. Novikov, Topology of foliations, Trans. Moscow Math. Soc. 14 (1965), 268-304. MR 0200938
- 13.
- V. Poénaru, Homotopy theory and differentiable singularities, Lecture Notes in Math., 197, Springer-Verlag, Berlin, 1971, pp. 106-132. MR 0285026
- 14.
- J. Pradines, Théorie de Lie pour les groupoïdes différentiables, calcul différentiel dans la catégorie des groupoïdes infinitésimaux, C. R. Acad. Sci. Paris 264 (1967), 245-248. MR 0216409
- 15.
- G. Reeb, Sur Certaines Propriétés Topologiques des Variétés Feuilletées, Hermann, Paris, 1952. MR 0055692
- 16.
- B. Reinhart, Foliated manifolds with bundle-like metrics, Ann. Math. 69 (1959), 119-132. MR 0107279
- 17.
- V. V. Solodov, Components of topological foliations, Mat. Sb (N.S.) 119(161) (1982), 340-354, Russian. MR 0678831 (85b:57033)
- 18.
- W. Thurston, A generalization of the Reeb stability theorem, Topology 13 (1974), 347-352. MR 0356087
- 19.
- -, The theory of foliations in codimension greater than one, Comment. Math. Helv. 49 (1974), 214-231. MR 0370619
- 20.
- -, Existence of codimension-one foliations, Ann. of Math. (2) 104 (1976), 249-268. MR 0425985
- 21.
- H. E. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom. 1 (1983), no. 3, 51-75. MR 0739904 (85j:57043)
- 22.
- -, The number of ends of the universal leaf of a Riemannian foliation, Differential geometry (College Park, Md., 1981/1982), Birkhäuser Boston, Mass., 1983, pp. 247-254. MR 0702537 (84i:57019)
Review Information:
Reviewer:
Lawrence Conlon
Affiliation:
Washington University in St. Louis
Email:
lc@math.wustl.edu
Journal:
Bull. Amer. Math. Soc.
42 (2005), 105-111
Published electronically:
October 5, 2004
Review copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
