The diffeology of Milnor's classifying space

Jean-Pierre Magnot; Jordan Watts

doi:10.1016/j.topol.2017.10.011

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arXiv · 1606.06680

The diffeology of Milnor's classifying space

Jean-Pierre Magnot·Jordan Watts

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Abstract

We define a diffeology on the Milnor classifying space of a diffeological group $G$, constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth principal bundles, we prove the existence of a diffeological connection on any principal bundle (with mild conditions on the bundles and groups), and apply the theory to some examples, including some infinite-dimensional groups, as well as irrational tori.

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Jean-Pierre Magnot, Jordan Watts. 2016-06-21. The diffeology of Milnor's classifying space. https://doi.org/10.1016/j.topol.2017.10.011

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