A spectral triple for noncommutative compact surfaces

Volume 120 / 2020

Fredy Díaz García, Elmar Wagner Banach Center Publications 120 (2020), 121-134 MSC: 58B34, 46L87. DOI: 10.4064/bc120-9

Abstract

A Dirac operator is presented that will yield a $1^+$-summable regular even spectral triple for all noncommutative compact surfaces defined as subalgebras of the Toeplitz algebra. Connes’ conditions for noncommutative spin geometries are analyzed and it is argued that the failure of some requirements is mainly due to a wrong choice of a noncommutative spin bundle.

Authors

  • Fredy Díaz GarcíaInstituto de Física y Matemáticas
    Universidad Michoacana de San Nicolás de Hidalgo
    Cd. Universitaria, Edificio C-3
    58040 Morelia, Michoacán, México
    ORCID: 0000-0001-6055-701X
    e-mail
  • Elmar WagnerInstituto de Física y Matemáticas
    Universidad Michoacana de San Nicolás de Hidalgo
    Cd. Universitaria, Edificio C-3
    58040 Morelia, Michoacán, México
    ORCID: 0000-0003-3932-9332
    e-mail

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