Helge Gloeckner

Open problems in the theory of infinite-dimensional Lie groups

In a preprint from 1982 preceding his well-known article from 1983, John Milnor discussed the foundations of the theory of infinite-dimensional Lie groups and formulated several fundamental problems, which are still beyond reach today. In the talk, I'll report on recent partial progress. In particular, I'll sketch why Hoelder continuous homomorphisms between infinite-dimensional Lie groups are smooth. Milnor's original question whether every continuous homomorphism is smooth remains open.