Stable splittings of 𝐵𝑂(2𝑛) and 𝐵𝑈(2𝑛)

Yan, Dung

doi:10.1090/S0002-9939-96-03205-4

Stable splittings of $\BO (2n)$ and $\BU (2n)$

Author: Dung Yung Yan
Journal: Proc. Amer. Math. Soc. 124 (1996), 1913-1915
MSC (1991): Primary 55P10
DOI: https://doi.org/10.1090/S0002-9939-96-03205-4
MathSciNet review: 1307573
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using the Snaith-Mitchell-Priddy splittings of $\BO (2n)$ and $\BU (2n)$ , we can give new stable splittings of $\BO (2n)$ and
$\BU (2n)$ respectively.

1. J. C. Becker and D. H. Gottlieb, Transfer maps for fibrations and duality, Compositio Math. 33 (1976), no. 2, 107–133. MR 436137
2. Hans-Werner Henn and Huỳnh Mui, Stable splittings for classifying spaces of alternating, special orthogonal and special unitary groups, Algebraic topology (Oaxtepec, 1991) Contemp. Math., vol. 146, Amer. Math. Soc., Providence, RI, 1993, pp. 143–158. MR 1224912, https://doi.org/10.1090/conm/146/01220
3. Stephen A. Mitchell and Stewart B. Priddy, Symmetric product spectra and splittings of classifying spaces, Amer. J. Math. 106 (1984), no. 1, 219–232. MR 729761, https://doi.org/10.2307/2374436
4. Stephen A. Mitchell and Stewart B. Priddy, Stable splittings derived from the Steinberg module, Topology 22 (1983), no. 3, 285–298. MR 710102, https://doi.org/10.1016/0040-9383(83)90014-9
5. Stephen A. Mitchell and Stewart B. Priddy, A double coset formula for Levi subgroups and splitting 𝐵𝐺𝐿_{𝑛}, Algebraic topology (Arcata, CA, 1986) Lecture Notes in Math., vol. 1370, Springer, Berlin, 1989, pp. 325–334. MR 1000386, https://doi.org/10.1007/BFb0085237
6. Victor P. Snaith, Algebraic cobordism and 𝐾-theory, Mem. Amer. Math. Soc. 21 (1979), no. 221, vii+152. MR 539791, https://doi.org/10.1090/memo/0221