Abstract
In Chapter 12 we gave the structure of various cobordism groups Ω G>* ≅ MG*(S°) = π*(MG) without giving any proofs. As it turns out, the determination of the homotopy groups π*(MG) is a problem to which the Adams spectral sequence is particularly well adapted for the reason that the homology H*(MG;Z p ) turns out to have a relatively simple structure as A*-comodule for G = O, U, SO and SU. In this chapter we shall use the Adams spectral sequence to compute Ωo, Ω.U and ΩSO We shall also prove the theorem of Stong and Hattori which says that π*(MU) → P(K*(MU)) is an isomorphism.
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References
J. F. Adams [7, 10, 12]
D. W. Anderson, E. H. Brown and F. P. Peterson [13, 14]
P. E. Conner and E. E. Floyd [31, 32]
A. Dold [33]
D. Husemoller [49]
A. Liulevicius [53, 54]
J.W. Milnor[61, 64]
J. W. Milnor and J. C. Moore [67]
R. E. Stong [83]
R. Thorn [84, 85]
C. T. C. Wall [89, 90, 92]
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© 2002 Springer-Verlag Berlin Heidelberg
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Switzer, R.M. (2002). Calculation of the Cobordism Groups. In: Algebraic Topology — Homotopy and Homology. Classics in Mathematics, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61923-6_21
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DOI: https://doi.org/10.1007/978-3-642-61923-6_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42750-6
Online ISBN: 978-3-642-61923-6
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