Journal of Mathematics of Kyoto University

On $[X, U(n)]$ when $\mathrm{dim} X$ is $2n+1$

Hiroaki Hamanaka

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Abstract

In this paper we investigate the homotopy set $[X,U(n)]$, where $X$ is a finite CW-complex with its dimension $2n + 1$ and $U(n)$ is the unitary group. This homotopy set has the group structure and can be described as a central extension using ordinary cohomology and $K$-theory.

Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 3 (2004), 655-667.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283088

Digital Object Identifier
doi:10.1215/kjm/1250283088

Mathematical Reviews number (MathSciNet)
MR2103787

Zentralblatt MATH identifier
1088.55009

Subjects
Primary: 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}
Secondary: 55P10: Homotopy equivalences 55Q05: Homotopy groups, general; sets of homotopy classes

Citation

Hamanaka, Hiroaki. On $[X, U(n)]$ when $\mathrm{dim} X$ is $2n+1$. J. Math. Kyoto Univ. 44 (2004), no. 3, 655--667. doi:10.1215/kjm/1250283088. https://projecteuclid.org/euclid.kjm/1250283088


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