Localization of grouplike function and section spaces with compact domain

Details Localization of grouplike function and section spaces with compact domain Localization of grouplike function and section spaces with compact domain

2009-08-22

arxiv.org/abs/0908.3243v1

Mathematics

Algebraic Topology

14 pages

Scientific paper

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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