Monday 5th of June 2023, 15:15-16:15 in HG03.085
Lennart Obster
Proving normal form results using Euler-like vector fields
An Euler-like vector field induces a tubular neighbourhood for which the vector field becomes the Euler
vector field on the normal bundle. In fact, this gives rise to a one-to-one correspondence between
Euler-like vector fields and (germs of) tubular neighbourhood embeddings (this was proven in a paper by
Henrique Bursztyn, Hudson Lima, and Eckhard Meinrenken in 2019). A strategy to prove normal form results
for a certain geometric structure is therefore: find an Euler-like vector field that is compatible with
the geometric structure. Eckhard Meinrenken, in a paper of 2021, clarified that this method also produces
lots of classical/known normal form results (often proofs of such results already used this method in
disguise). This allows for a clear, down-to-earth introduction to this idea.
In this talk we will introduce Euler-like vector fields and discuss applications to normal form results.