The diffeology of Milnor's classifying space

Jean Pierre Magnot, Jordan Watts

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish
Pages (from-to)189-213
Number of pages25
JournalTopology and its Applications
StatePublished - Dec 1 2017


  • Classifying space
  • Diffeological group
  • Diffeology
  • Lie group
  • Universal bundle


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