Uniqueness of infinite deloopings for K-theoretic spaces

Aldridge Knight Bousfield

Vol. 129 (1987), No. 1, 1–31

DOI: 10.2140/pjm.1987.129.1

Abstract

A functor Φ_p is constructed from spaces to spectra such that, for each spectrum X, Φ_pΩ^∞X is the p-adic completion of the K-theoretic localization of X. This functor is used to obtain uniqueness results for infinite deloopings of K-theoretic spaces and maps, thereby generalizing results of Adams-Priddy and Madsen-Snaith-Tornehave. Non-unique deloopings of K-theoretic maps are shown to involve phantom maps of spectra, and such maps are analyzed.

Mathematical Subject Classification 2000

Primary: 55P60

Secondary: 55N15, 55P47, 55R45

Milestones

Received: 25 November 1985

Published: 1 September 1987