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Gromov-Hausdorff distance for quantum metric spaces


About this Title

Marc A. Rieffel

Publication: Memoirs of the American Mathematical Society
Publication Year 2004: Volume 168, Number 796
ISBNs: 978-0-8218-3518-0 (print); 978-1-4704-0394-2 (online)
DOI: http://dx.doi.org/10.1090/memo/0796
MathSciNet review: 2055927
MSC (2000): Primary 46L87; Secondary 53C23, 58B34, 60B10

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Table of Contents


Chapters

  • Gromov-Hausdorff distance for quantum metric spaces
  • 1. Introduction
  • 2. Compact quantum metric spaces
  • 3. Quotients (= “subsets”)
  • 4. Quantum Gromov-Hausdorff distance
  • 5. Bridges
  • 6. Isometries
  • 7. Distance zero
  • 8. Actions of compact groups
  • 9. Quantum tori
  • 10. Continuous fields of order-unit spaces
  • 11. Continuous fields of lip-norms
  • 12. Completeness
  • 13. Finite approximation and compactness
  • Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
  • 0. Introduction
  • 1. The quantum metric spaces
  • 2. Choosing the bridge constant $\gamma $
  • 3. Compact semisimple Lie groups
  • 4. Covariant symbols
  • 5. Contravariant symbols
  • 6. Conclusion of the proof of Theorem 3.2

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