Existence and rigidity of quantum isometry groups for compact metric spaces

Abstract

We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed probability measure. In the former case it also follows from recent results of the second author that the quantum isometry group is classical, i.e. the commutative $C^{\ast }$-algebra of continuous functions on the Riemannian isometry group.

30 pages + references; edits after referee comments; to appear in Communications in Mathematical Physics

References in corpus (3)

• Quantum Group of Isometries in Classical and Noncommutative Geometry
• On quantum symmetries of compact metric spaces
• Quantum rigidity of negatively curved manifolds

Cited by in corpus (1)

• Quantum isometries and loose embeddings