³ÉÈË´óƬ

Dynamics, Geometry and Groups Seminar

Speaker: David Miyamoto (³ÉÈË´óƬ)

Title: The smooth structure of a Lie group and its quotients

Abstract:
Given a Lie group G and a closed normal subgroup H, the quotient G/H is a Lie group with Lie algebra Lie(G)/Lie(H). When H is not closed (e.g. H could be dense), then G/H is no longer a manifold, and its quotient topology could even be trivial. I will discuss how, by instead viewing G/H as a diffeological space, we may always treat this quotient group as a smooth group with the expected Lie algebra. Specifically: G/H is a quasifold group, meaning it is locally modeled by quotients of R^n by countable affine actions (joint with Yi Lin), and it is elastic, meaning we have a Lie functor for which Lie(G/H) = Lie(G)/Lie(H) (invoking results of Christian Blohmann). Time permitting, I will indicate how this generalizes to the case of infinite-dimensional Banach Lie groups.