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Modular Gaussian curvature

In: Advances in Noncommutative Geometry

Author

Listed:
  • Matthias Lesch

    (Universität Bonn, Mathematisches Institut)

  • Henri Moscovici

    (The Ohio State University, Department of Mathematics)

Abstract

This is a brief survey of the main developments that led to the emergence of the quantized analogue of Gaussian curvature for the noncommutative torus and to its current understanding. It highlights the role of Connes’ pseudodifferential calculus as the crucial technical tool for the explicit computation of the modular Gaussian curvature, the effectiveness of the variational methods, and it sheds more light on the intrinsic geometric meaning of the Morita equivalence in this context.

Suggested Citation

  • Matthias Lesch & Henri Moscovici, 2019. "Modular Gaussian curvature," Springer Books, in: Ali Chamseddine & Caterina Consani & Nigel Higson & Masoud Khalkhali & Henri Moscovici & Guoliang Yu (ed.), Advances in Noncommutative Geometry, pages 463-490, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-29597-4_8
    DOI: 10.1007/978-3-030-29597-4_8
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