JournalsjncgVol. 15 , No. 2pp. 735–759

Quasifolds, diffeology and noncommutative geometry

  • Patrick Iglesias-Zemmour

    The Hebrew University of Jerusalem, Israel
  • Elisa Prato

    Università di Firenze, Italy
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Abstract

After embedding the objects quasifolds into the category {\{Diffeology}\}, we associate a C\boldsymbol{C}^*-algebra with every atlas of any quasifold, and show how different atlases give Morita equivalent algebras. This builds a new bridge between diffeology and noncommutative geometry – beginning with the today classical example of the irrational torus – which associates a Morita class of C\boldsymbol{C}^*-algebras with a diffeomorphic class of quasifolds.

Cite this article

Patrick Iglesias-Zemmour, Elisa Prato, Quasifolds, diffeology and noncommutative geometry. J. Noncommut. Geom. 15 (2021), no. 2 pp. 735–759

DOI 10.4171/JNCG/419