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ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Some applications of Landweber-Novikov operations


Author: David M. Segal
Journal: Proc. Amer. Math. Soc. 54 (1976), 342-344
DOI: https://doi.org/10.1090/S0002-9939-1976-0388419-5
MathSciNet review: 0388419
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Abstract | References | Additional Information

Abstract: Previous results on the characteristic numbers of $ Sp$-manifolds are extended in three different ways. I. It is shown that the primitive symplectic Pontrjagin class evaluated on a $ 4({2^j} - 1)$ dimensional $ Sp$-manifold always gives a number divisible by $ 8$. This forms an analogue to a well-known result of Milnor concerning $ U$-manifolds. II. It is shown that some of the results of Floyd as well as an analogue of the previous result can be obtained for 'pseudo-symplectic' manifolds. III. Results are generalised to $ (Sp,fr)$ manifolds.


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

  • [1] J. F. Adams, S. P. Novikov's work on operations on complex cobordism, University of Chicago Lecture Notes, 1967.
  • [2] E. E. Floyd, Stiefel-Whitney numbers of quaternionic and related manifolds, Trans. Amer. Math. Soc. 155(1971), 77-94. MR42 #8509. MR 0273632 (42:8509)
  • [3] D. M. Segal, Divisibility conditions on characteristic numbers of stably symplectic manifolds, Proc. Amer. Math. Soc. 27(1971), 411-415. MR42 #5282. MR 0270393 (42:5282)
  • [4] R. E. Stong, Some remarks on symplectic cobordism, Ann. of Math. (2)86(1967), 425-433. MR36 #2162. MR 0219079 (36:2162)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0388419-5
Keywords: Landweber-Novikov operation, symplectic manifold, pseudo-symplectic manifold, symplectic-framed manifold
Article copyright: © Copyright 1976 American Mathematical Society

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