透過上同調作為外代數 E=ℤ/2<Q₀, Q₁> 模的代數分解，我們完整的分解了BSO(2n+1)的複連通K理論。

Through the algebraic splitting of the cohomology over the exterior algebra E=ℤ/2<Q₀, Q₁>, we give the complete stable splitting of the complex connective K-theory of BSO(2n+1), n≥1.

1.Introduction ---------------------------------------------page 1
2.The Adams spectral sequences for bu∧X --------------------page 4
3.The E₂ term of the Adams spectral sequences for bu∧BO(n) -page 7
4.The map Bg_{2n}:BO(2n)→BSO(2n+1) ------------------------page 11
5.Proof of Theorem A ---------------------------------------page 15
6.Proof of Theorem B ---------------------------------------page 17
7.Reference-------------------------------------------------page 21

[1] J. F. Adams, Stable homotopy and generalized homology, Chicago Lecture Notes in Math. Univ. Chicago Press, 1974.
[2] B. R. Burner and J. P. C. Greenless, Connective K-theory of …nite groups, Mem. Amer. Math. Soc. 165 (2003).
[3] A. Liulevicius, The cohomology ofMassey-Peterson algebras, Math. Zeitschr. 105 (1968), 226-256.
[4] R. Ming, Yoneda products in the Cartan-Eilenberg change of rings spectral sequence with applications to BPBO(n), Trans. Amer. Math. Soc. 219 (1976), 235-252.
[5] J. W. Milnor, The Steenrod algebra and its dual, Ann. Math. 67 (1958), 150-171.
[6] E. Ossa, Connective K-theory of elementary abelian groups, Transformation Groups, Osaka 1987, K. Kawakubo (ed.), Springer Lecture Notes in Mathematics 1375 (1989), 150-171.
[7]W. StephenWilson and D. Y. Yan, Stable splitting of the complex connective K-theory of BO(n), Topology and its Applications. 159 (2012), 1409-1414.
[8] R. M. Switzer, Homology comodules, Inventions, Math. 20 (1973), 97-102.
[9]W. T.Wu, Classes caractéristiques et i-carrés d’une variété, Comptes Rendus 230 (1950), 508-511.
[10] D. Y. Yan, Stable splitting of the quotient spaces BO(2n)=BO(2n􀀀2) and BU(np)=BU(np 􀀀 p). Form Math. 11 (1999), 211-227.
[11] Y. C. Tseng and D. Y. Yan, Stable splitting of the complex connective K-theory of BG for some in…nite groups G, Bulletin of the institute of Mathematics, Academis Sinica (new series) Vol. 2 (2007), No. 3, pp. 687-712.
[12] Tsung-Hsuan Wu, Stable splittings of the complex connective K-theory of BSO(2n + 1), Math. J. Okayama Univ. 60 (2018), 73-89.
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