Divisibility conditions on characteristic numbers of stably symplectic manifolds
HTML articles powered by AMS MathViewer
- by D. M. Segal
- Proc. Amer. Math. Soc. 27 (1971), 411-415
- DOI: https://doi.org/10.1090/S0002-9939-1971-0270393-9
- PDF | Request permission
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
- E. E. Floyd, Stiefel-Whitney numbers of quaternionic and related manifolds, Trans. Amer. Math. Soc. 155 (1971), 77–94. MR 273632, DOI 10.1090/S0002-9947-1971-0273632-8
- P. S. Landweber, Cobordism operations and Hopf algebras, Trans. Amer. Math. Soc. 129 (1967), 94–110. MR 219062, DOI 10.1090/S0002-9947-1967-0219062-5
- Arunas Liulevicius, Notes on homotopy of Thom spectra, Amer. J. Math. 86 (1964), 1–16. MR 166787, DOI 10.2307/2373032
- D. M. Segal, On the symplectic cobordism ring, Comment. Math. Helv. 45 (1970), 159–169. MR 263094, DOI 10.1007/BF02567323
- R. E. Stong, Some remarks on symplectic cobordism, Ann. of Math. (2) 86 (1967), 425–433. MR 219079, DOI 10.2307/1970608
- René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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