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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the stability of equivariant foliations


Author: Janez Mrcun
Journal: Proc. Amer. Math. Soc. 125 (1997), 1561-1570
MSC (1991): Primary 57R30, 57S25
MathSciNet review: 1402875
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Abstract: We prove an equivariant version of the Reeb-Thurston stability theorem for foliations invariant under an action of a discrete group.


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  • 1. M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), no. 1, 1–28. MR 721448 (85e:58041), http://dx.doi.org/10.1016/0040-9383(84)90021-1
  • 2. Raoul Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology (Second Latin American School in Math., Mexico City, 1971), Springer, Berlin, 1972, pp. 1–94. Lecture Notes in Math., Vol. 279. Notes by Lawrence Conlon, with two appendices by J. Stasheff. MR 0362335 (50 #14777)
  • 3. César Camacho and Alcides Lins Neto, Geometric theory of foliations, Birkhäuser Boston Inc., Boston, MA, 1985. Translated from the Portuguese by Sue E. Goodman. MR 824240 (87a:57029)
  • 4. Alain Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360. MR 823176 (87i:58162)
  • 5. W. T. van Est, Rapport sur les 𝑆-atlas, Astérisque 116 (1984), 235–292 (French). Transversal structure of foliations (Toulouse, 1982). MR 755174 (86e:58003)
  • 6. André Haefliger, Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv. 32 (1958), 248–329 (French). MR 0100269 (20 #6702)
  • 7. Serge Lang, Differential manifolds, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0431240 (55 #4241)
  • 8. I. Moerdijk, Classifying toposes and foliations. Ann. Inst. Fourier, Grenoble 41, 1 (1991), 189-209. MR 91i:57028
  • 9. 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 (89b:53054)
  • 10. J. Mrcun, An extension of the Reeb stability theorem. Topology Appl. 70 (1996), 25-55. CMP 96:12
  • 11. Georges Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Actualités Sci. Ind., no. 1183, Hermann & Cie., Paris, 1952 (French). Publ. Inst. Math. Univ. Strasbourg 11, pp. 5–89, 155–156. MR 0055692 (14,1113a)
  • 12. W. P. Thurston, A generalization of the Reeb stability theorem. Topology 13 (1974), 347-352.

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Additional Information

Janez Mrcun
Email: janez.mrcun@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03971-3
PII: S 0002-9939(97)03971-3
Keywords: Foliation, group action
Received by editor(s): December 1, 1995
Additional Notes: This work was partially supported by the Ministry of Science of Slovenia
Communicated by: Ronald Stern
Article copyright: © Copyright 1997 American Mathematical Society