On certain C0-aspects of contactomorphism groups

We will explore certain C0-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is reflected in the group of contact homeomorphisms. We will also define a new conjugation-invariant norm on the group of smooth contactomorphisms and study its relation to the contact fragmentation norm. The main technical ingredient is a result stating that Sandons spectral norm is C0-locally bounded. The talk is based on a joint work with Baptiste Serraille.