On the complex bordism of Eilenbeg-Mac Lane spaces and connective coverings of $\textrm {BU}$
HTML articles powered by AMS MathViewer
- by Peter S. Landweber PDF
- Trans. Amer. Math. Soc. 157 (1971), 63-71 Request permission
Abstract:
Explicit computations show that the universal coefficient spectral sequence from complex bordism to integral homology collapses for the spectra $K(Z)$ and bu, and also for their $\bmod p$ reductions. Moreover the complex bordism modules of these spectra have infinite projective dimension.References
- J. F. Adams, On Chern characters and the structure of the unitary group, Proc. Cambridge Philos. Soc. 57 (1961), 189–199. MR 121795, DOI 10.1017/s0305004100035052
- P. E. Conner and E. E. Floyd, The relation of cobordism to $K$-theories, Lecture Notes in Mathematics, No. 28, Springer-Verlag, Berlin-New York, 1966. MR 0216511
- P. E. Conner and Larry Smith, On the complex bordism of finite complexes, Inst. Hautes Études Sci. Publ. Math. 37 (1969), 117–221. MR 267571
- Akio Hattori, Integral characteristic numbers for weakly almost complex manifolds, Topology 5 (1966), 259–280. MR 192517, DOI 10.1016/0040-9383(66)90010-3
- Peter S. Landweber, Steenrod representability of stable homology, Proc. Amer. Math. Soc. 18 (1967), 523–529. MR 229241, DOI 10.1090/S0002-9939-1967-0229241-4
- Saunders Mac Lane, Homology, Die Grundlehren der mathematischen Wissenschaften, Band 114, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156879
- John Milnor, The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 150–171. MR 99653, DOI 10.2307/1969932
- Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 157 (1971), 63-71
- MSC: Primary 55.52; Secondary 57.00
- DOI: https://doi.org/10.1090/S0002-9947-1971-0275434-5
- MathSciNet review: 0275434