Regularity properties of infinite-dimensional Lie groups

by Helge Gloeckner

Thursday 16 May 2024, 16:15 → 17:15 Europe/Zurich

Sitzungszimmer (MI)

Consider a Lie group G modeled on a locally convex space, with neutral element e. A time-dependent left-invariant vector field on G is determined by a path c in the Lie algebra L(G) of G. If an integral curve starting at e exists for each smooth path c in L(G) and depends smoothly on c, then G is called regular. The question whether each Lie group (modeled on a sufficiently complete locally convex space) is regular has remained open since the 1980s, when John Milnor first introduced the concept. It is one of the miracles of the theory that regularity could be established for all concrete examples, despite the absence of a general argument. In fact, most examples even have stronger regularity properties: smooth paths can be replaced with continuous paths in the definition of regularity, or with Bochner integrable functions.
The talk will provide an introduction to the topic and describe some recent results.