On the entropy norm on the group of diffeomorphisms of closed oriented surface

TL;DR

This paper proves that the entropy norm on the group of diffeomorphisms of a closed orientable surface of positive genus can grow arbitrarily large, indicating unbounded complexity in the group's structure.

Contribution

It establishes the unboundedness of the entropy norm on the diffeomorphism group of closed orientable surfaces of positive genus, a new result in geometric group theory.

Findings

Entropy norm is unbounded on the group of surface diffeomorphisms.

The result applies to surfaces of positive genus.

Provides insights into the complexity of surface diffeomorphism groups.

Abstract

We prove that the entropy norm on the group of diffeomorphisms of a closed orientable surface of positive genus is unbounded.