Bott maps and the complex projective plane: A construction of R. Wood's equivalences
type: Item
instance of: scholarly article
title: Bott maps and the complex projective plane: A construction of R. Wood's equivalences
zbMATH Open document ID: 0585.55015
author: Minato Yasuo
published in: Pacific Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A well-known result of R. Wood in K-theory implies that the unitary group U(\(\infty)\) is homotopy-equivalent to the space of based maps \({\mathbb{P}}_ 2{\mathbb{C}}\to G(\infty)\) where G(\(\infty)\) is either the orthogonal group O(\(\infty)\) or the symplectic group Sp(\(\infty)\). In the present paper an explicit construction of such homotopy equivalences is given, and Wood's theorem is proved by the same method as in the author's previous paper [Publ. Res. Inst. Math. Sci. 19, 317-326 (1983; Zbl 0516.55007)].
Mathematics Subject Classification ID: 55R50
Mathematics Subject Classification ID: 55P10
zbMATH DE Number: 3938040
zbMATH Keywords: K-theory
zbMATH Keywords: unitary group
zbMATH Keywords: orthogonal group
zbMATH Keywords: symplectic group
zbMATH Keywords: Bott map
zbMATH Keywords: complex projective plane
MaRDI profile type: Publication
full work available at URL: pjm.1987.128.379
OpenAlex ID: W1969523559
DOI: 10.2140/PJM.1987.128.379
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description: scientific article; zbMATH DE number 3938040