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Transactions of the American Mathematical Society

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Residue classes of Lagrangian subbundles and Maslov classes


Author: Haruo Suzuki
Journal: Trans. Amer. Math. Soc. 347 (1995), 189-202
MSC: Primary 57R20; Secondary 58F05
DOI: https://doi.org/10.1090/S0002-9947-1995-1282897-1
MathSciNet review: 1282897
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Abstract: For Lagrangian subbundles with singularities in symplectic vector bundles, explicit formulas of relation between their residue classes and Maslov classes outside singularities are obtained. Then a Lagrangian subbundle with singularity is constructed where all possible Maslov classes are nonzero but residue classes vanish for dimension $ > 2$. Moreover, a Lagrangian immersion with singularity is constructed, where the similar property for the associated Maslov classes and residue classes is shown.


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  • [B-T] R. Bott and L. W. Tu, Differential forms in algebraic topology, Springer, Berlin and New York, 1982. MR 658304 (83i:57016)
  • [C-S] S. S. Chern and J. Simons, Characteristic forms and geometric invariants, Ann. of Math. (2) 99 (1974), 48-69. MR 0353327 (50:5811)
  • [K-T] F. Kamber and Ph. Tondeur, Foliated bundles and characteristic classes, vol. 493, Lecture Notes in Math., Springer, Berlin and New York, 1975. MR 0402773 (53:6587)
  • [L1] D. Lehmann, Variété stratifiées $ {C^\infty }$: Intégration de Čech-de Rham, et théorie de Chern-Weil, Geometry and Topology of Submanifolds, II (Avignon, 1988), World Scientific, Teaneck, NJ, 1990, pp. 205-248. MR 1068742 (92a:58007)
  • [L2] D. Lehmann, Classes caractéristiques residuelles, Differential Geometry and Its Applications, World Scientific, Singapore, 1990, pp. 85-108. MR 1062009 (91e:57043)
  • [M] J. McCleary, User's guide to spectral sequences, Publish or Perlish, Wilmington, DE, 1985. MR 820463 (87f:55014)
  • [M-N] J.-M. Morvan and L. Niglio, Classes caractéristiques des couples de sous-fibrés Lagrangiens, Ann. Inst. Fourier Grenoble 36 (1986), 193-209. MR 850751 (87m:58165)
  • [Se] J.-P. Serre, Homologie singulière des espaces fibrés, Ann. of Math. 54 (1951), 425-505. MR 0045386 (13:574g)
  • [Su] H. Suzuki, Chern-Simons-Malsov classes of some symplectic vector bundles, Proc. Amer. Math. Soc. 117 (1993), 541-546. MR 1124152 (93d:57055)
  • [V] I. Vaisman, Symplectic geometry and secondary characteristic classes, Birkhäuser, Boston and Basel, 1987. MR 932470 (89f:58062)
  • [W] A. Weil, Sur les théorèmes de de Rham, Comment. Math. Helv. 26 (1952), 119-145. MR 0050280 (14:307b)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1282897-1
Article copyright: © Copyright 1995 American Mathematical Society

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