Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] R. Bott, Lectures on characteristic classes of foliations, Lecture Notes in Math., vol. 279, Springer-Verlag, 1972. MR 0362335 (50:14777)
  • [2] M. Gromov, Volume and bounded cohomology, Publ. Math. Inst. Hautes Études Sci. 56 (1982), 5-100. MR 686042 (84h:53053)
  • [3] S. Hurder and Y. Mitsumatsu (in preparation).
  • [4] J. W. 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] D. Sullivan, A generalization of Milnor's inequality concerning affine foliations and affine manifolds, Comment. Math. Helv. 51 (1976), 183-189. MR 0418119 (54:6163)
  • [7] -, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math. 36 (1976), 225-255. MR 0433464 (55:6440)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R30, 28D15, 57R20

Retrieve articles in all journals with MSC: 57R30, 28D15, 57R20

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society