The study of the representations theoretic properties of the group of diffeormorphisms of locally compact non compact Riemmanian manifolds which equal to the identity outside a compact set is is linked to a natural quasi invariant action of the group which moves all points of a Poisson point process according to the diffeomorphism (Gelfand-Graev-Vershik and Goldin et al.).

Neretin noticed that the local diffeomorphism group is a subgroup of a larger group which he called GMS and that GMS also acts in a similar manner on the Poisson point process.

In this talk we will present the largest group which acts by such quasi-invariant automorphisms and discuss the following facts and results:

• Neretin’s group and the larger group are Polish groups.

• In the case when M is the real line, the group of local diffeomorphisms is nowhere dense in Neretin’s group and dense in the larger group (with respect to its Polish topology).

•The ergodic automorphisms are generic in the larger group and nowhere dense in Neretin’s group.

All relevant notions and background will be defined.

This is joint work with A. Danilenko and E. Roy.

Neretin noticed that the local diffeomorphism group is a subgroup of a larger group which he called GMS and that GMS also acts in a similar manner on the Poisson point process.

In this talk we will present the largest group which acts by such quasi-invariant automorphisms and discuss the following facts and results:

• Neretin’s group and the larger group are Polish groups.

• In the case when M is the real line, the group of local diffeomorphisms is nowhere dense in Neretin’s group and dense in the larger group (with respect to its Polish topology).

•The ergodic automorphisms are generic in the larger group and nowhere dense in Neretin’s group.

All relevant notions and background will be defined.

This is joint work with A. Danilenko and E. Roy.

## Date:

Thu, 10/05/2018 - 14:30 to 15:30

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem