Abstract We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric measure spaces appropriately, the subset consisting of those with trivial compact quantum automorphism group is of 2nd Baire category. The latter result can be paraphrased as saying that “most” compact metric measure spaces have no (quantum) symmetries; in particular, they also have trivial ordinary (i.e., classical) automorphism group.
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The Lorentzian scattering rigidity problem and rigidity of stationary metrics
- Award ID(s):
- 2154489
- PAR ID:
- 10586469
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- The Journal of Geometric Analysis
- Volume:
- 34
- Issue:
- 9
- ISSN:
- 1050-6926
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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