群函数的局部化与具有紧域的截空间
Localization of grouplike function and section spaces with compact domain
摘要：
本文将Hilton-Mislin-Roitberg和Moller在CW范畴外提出的函数和截面空间的标准局部化理论推广到了紧度量域中存在类群结构的情形。我们研究了直接推广主丛规范群的两种情况下的应用。我们证明了一个身份的幺半群的纤维同伦自等价的Hurewicz纤维化-由于Gottlieb和Booth-Heath-Morgan-Piccinini在CW范畴-在紧凑的情况下。这导致了一个扩展的本地化结果为这个幺半群。我们还得到了一个扩展的局部化理论的部分组的纤维群。我们给出了有理同伦理论的两个应用。
英文摘要：
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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