Infinite-dimensional geometry 3.3. Regular Lie groups and the Lie group exponential
Channel: Alexander Schmeding
Date: 2020-10-17

The notion of regularity allows us to solve Lie type differential equations on infinite-dimensional Lie groups. We show how this can be exploited to establish completeness of left-invariant vector fields and the construction of the Lie group exponential map. Furthermore, we discuss cases in which the exponential map fails to be a local diffeomorphism around the identity.

This is part of the course MAT331: Topics in Analysis at the University of Bergen in Fall 2020. 
This course (and the lecture) was supported by Trond Mohn foundation within the Pure Mathematics in Norway program (https://www.puremath.no/).