ar X iv : 0 90 8 . 32 43 v 1 [ m at h . A T ] 2 2 A ug 2 00 9 Localization of grouplike function and section spaces with compact domain
نویسندگان
چکیده
By recent results in [19], the standard localization theory for function and section spaces due to Hilton-Mislin-Roitberg and Möller extend 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 aut(ξ) of fibre-homotopy self-equivalences of a Hurewicz fibration ξ — due to Gottlieb and Booth-Heath-Morgan-Piccinini in the CW category — in the compact case. This leads to an extended localization result for aut(ξ). We also obtain an extended localization theory for groups of sections Γ(ζ) of a fibrewise group ζ. We give two applications in rational homotopy theory.
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