Fiber bundles over Alexandroff spaces

Nicolás Cianci; Miguel Ottina

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arXiv · 1907.03614

Fiber bundles over Alexandroff spaces

Nicolás Cianci·Miguel Ottina

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Abstract

We introduce a topological variant of the Grothendieck construction which serves to represent every fiber bundle over an Alexandroff space. Using this result we give a classification theorem for fiber bundles over Alexandroff spaces with T$_0$ fiber and we construct a universal bundle for bundles with T$_0$ fiber over posets which are cofibrant objects of the category of small categories. Moreover, we prove that our construction induces an equivalence of categories between a suitable category of functors and the category of fiber bundles over a fixed Alexandroff space. In addition, we prove that any fiber bundle over an Alexandroff space is a fibration.

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BibTeX RIS

Nicolás Cianci, Miguel Ottina. 2019-07-08. Fiber bundles over Alexandroff spaces. https://arxiv.org/abs/1907.03614

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