Localization of grouplike function and section spaces with compact domain

Claude L. Schochet; Samuel B. Smith

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arXiv · 0908.3243

Localization of grouplike function and section spaces with compact domain

Claude L. Schochet·Samuel B. Smith

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Abstract

We extend the standard localization theory for function and section spaces due to Hilton-Mislin-Roitberg and Moller outside the CW category to the case of compact metric domain in the presence of a grouplike structure. We study applications in two cases directly generalizing the gauge group of a principal bundle. We prove an identity for the monoid of fibre-homotopy self-equivalences of a Hurewicz fibration -- due to Gottlieb and Booth-Heath-Morgan-Piccinini in the CW category -- in the compact case. This leads to an extended localization result for this monoid. We also obtain an extended localization theory for groups of sections of a fibrewise group. We give two applications in rational homotopy theory.

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BibTeX RIS

Claude L. Schochet, Samuel B. Smith. 2009-08-22. Localization of grouplike function and section spaces with compact domain. https://arxiv.org/abs/0908.3243

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