A note on the divisibility of certain Chern numbers

Charitos, Leonidas; Papastavridis, Stavros

doi:10.1090/S0002-9939-1982-0637182-1

A note on the divisibility of certain Chern numbers
HTML articles powered by AMS MathViewer

by Leonidas Charitos and Stavros Papastavridis

Proc. Amer. Math. Soc. 84 (1982), 272-274

DOI: https://doi.org/10.1090/S0002-9939-1982-0637182-1

PDF | Request permission

Abstract:

If $M$ is a weakly almost complex manifold, then ${c_r}(M) \in {H^{24}}(M;Z)$ is the $r$th Chern class of its normal bundle. Theorem 1. If $m$, $r$ are natural numbers with $r \leqslant m$, then there exists a $2m$-fold ${M_0}$, compact, closed and weakly almost complex, so that the normal characteristic number $\left \langle {{c_r}({M_0}){c_{m - r}}({M_0})} \right .$, $\left . {[{M_0}]} \right \rangle$ is a power of 2.

References

Edgar H. Brown Jr. and Franklin P. Peterson, Relations among characteristics classes. II, Ann. of Math. (2) 81 (1965), 356–363. MR 176490, DOI 10.2307/1970620
Arunas Liulevicius, On the birth and death of elements in complex cobordism, Conference on homotopy theory (Evanston, Ill., 1974) Notas Mat. Simpos., vol. 1, Soc. Mat. Mexicana, México, 1975, pp. 83–102. MR 761722
J. Milnor, On the cobordism ring $\Omega ^{\ast }$ and a complex analogue. I, Amer. J. Math. 82 (1960), 505–521. MR 119209, DOI 10.2307/2372970
E. Rees and E. Thomas, On the divisibility of certain Chern numbers, Quart. J. Math. Oxford Ser. (2) 28 (1977), no. 112, 389–401. MR 467771, DOI 10.1093/qmath/28.4.389