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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the self-intersections of foliation cycles


Author: Yoshihiko Mitsumatsu
Journal: Trans. Amer. Math. Soc. 334 (1992), 851-860
MSC: Primary 57R30; Secondary 28D15, 57R20
MathSciNet review: 1183731
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Abstract: The existence of a transverse invariant measure imposes a strong restriction on the transverse complexity of a foliated manifold. The homological self-intersection of the corresponding foliation cycle measures the complexity around its support. In the present paper, the vanishing of the self-intersection is proven under some regularity condition on the measure.


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  • [1] 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)
  • [2] Michael Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982), 5–99 (1983). MR 686042 (84h:53053)
  • [3] S. Hurder and Y. Mitsumatsu (in preparation).
  • [4] John Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958), 215–223. MR 0095518 (20 #2020)
  • [5] Y. Mitsumatsu, Self-intersections and transverse euler numbers of foliation cycles, Thesis, University of Tokyo, 1985.
  • [6] Dennis Sullivan, A generalization of Milnor’s inequality concerning affine foliations and affine manifolds, Comment. Math. Helv. 51 (1976), no. 2, 183–189. MR 0418119 (54 #6163)
  • [7] Dennis Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math. 36 (1976), 225–255. MR 0433464 (55 #6440)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1183731-8
PII: S 0002-9947(1992)1183731-8
Article copyright: © Copyright 1992 American Mathematical Society