Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Divisibility conditions on characteristic numbers of stably symplectic manifolds


Author: D. M. Segal
Journal: Proc. Amer. Math. Soc. 27 (1971), 411-415
MSC: Primary 57.32
DOI: https://doi.org/10.1090/S0002-9939-1971-0270393-9
MathSciNet review: 0270393
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that every cohomology characteristic number of an $ 8k + 4$ [resp. $ 16k + 8$] dimensional stably symplectic manifold is divisible by 4 [resp. 2] and that certain characteristic numbers of $ 2$-dimensional stably symplectic manifolds are divisible by 2 and 4. The proofs depend on symplectic cobordism operations. Using explicit manifold constructions of Stong [5] it is shown that these results are to a large extent the best possible.


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

  • [1] E. E. Floyd, Stiefel-Whitney numbers of quaternionic and related manifolds, (to appear). MR 0273632 (42:8509)
  • [2] P. S. Landweber, Cobordism operations and Hopf algebras, Trans. Amer. Math. Soc. 129 (1967), 94-110. MR 36 #2145. MR 0219062 (36:2145)
  • [3] A. Liulevicius, Notes on homotopy of Thom spectra, Amer. J. Math. 86 (1964), 1-6. MR 29 #4060. MR 0166787 (29:4060)
  • [4] D. M. Segal, On the symplectic cobordism ring, Comment. Math. Helv. 45 (1970), 159-169. MR 0263094 (41:7699)
  • [5] R. E. Stong, Some remarks on symplectic cobordism, Ann. of Math. (2) 86 (1967), 425-433. MR 36 #2162. MR 0219079 (36:2162)
  • [6] R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86. MR 15, 890. MR 0061823 (15:890a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57.32

Retrieve articles in all journals with MSC: 57.32


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0270393-9
Keywords: Symplectic cobordism, stably symplectic manifolds, symplectic Pontrjagin numbers, characteristic numbers
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society