The Algebraic Splitting of $\mathit{bu}\wedge{BSO(2n)}$
by I-Ming Tsai   Tsung-Hsuan Wu   Dong Yung Yan  

Vol. 15 No. 2 (2020) P.163~P.175

DOI:	https://doi.org/10.21915/BIMAS.2020204
	10.21915/BIMAS.2020204

ABSTRACT

We show that the mod 2 cohomology of $\mathit{bu}\wedge{BSO(2n)}$ is isomorphic to a direct sum of $E$-modules, $E=\mathbb{Z}/2\langle{Q_{0},Q_{1}}\rangle$, $n\geq2$. This would give the algebraic splitting of the complex connective $K$-theory of $BSO(2n)$.

KEYWORDS
stable splitting, complex connective K-theory, Stifel-Whitney classes

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 55N20

MILESTONES

Received: 2020-04-10
Revised :
Accepted: 2020-06-15

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