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Rational Cup Product and Algebraic K0-Groups of Rings of Continuous Functions

Part of: Grothendieck groups and $K_0$ Homological methods Fiber spaces and bundles

Published online by Cambridge University Press:  10 April 2018

Hiroshi Kihara  and
Nobuyuki Oda
Hiroshi Kihara*
Affiliation:
Center for Mathematical Sciences, University of Aizu, Tsuruga, Ikki-machi, Aizu-Wakamatsu City, 965-8580 Fukushima, Japan ([email protected])
Nobuyuki Oda
Affiliation:
Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan ([email protected])
*
*Corresponding author.
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Abstract

A connected space is called a C0-space if its rational cup product is trivial. A characterizing property of C0-spaces is obtained. This property is used to calculate the algebraic K0-group K0(C𝔽(X)) of the ring of continuous functions for infinite-dimensional complexes X.

Keywords

K-groupSerre–Swan theoremSullivan conjecture

MSC classification

Primary: 55R50: Stable classes of vector space bundles, $K$-theory
Secondary: 16E20: Grothendieck groups, $K$-theory, etc. 19A49: $K_0$ of other rings
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 3 , August 2018 , pp. 607 - 622
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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