Spectral metric and Einstein functionals for the Hodge–Dirac operator

  • Ludwik Dąbrowski

    SISSA (Scuola Internazionale Superiore di Studi Avanzati), Trieste, Italy
  • Andrzej Sitarz

    Jagiellonian University, Kraków, Poland
  • Paweł Zalecki

    Jagiellonian University, Kraków, Poland
Spectral metric and Einstein functionals for the Hodge–Dirac operator cover
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Abstract

We examine the metric and Einstein bilinear functionals of differential forms introduced by Dąbrowski et al. (2023), for the Hodge–Dirac operator on an oriented, closed, even-dimensional Riemannian manifold. We show that they are equal (up to a numerical factor) to these functionals for the canonical Dirac operator on a spin manifold. Furthermore, we demonstrate that the spectral triple for the Hodge–Dirac operator is spectrally closed, which implies that it is torsion-free.

Cite this article

Ludwik Dąbrowski, Andrzej Sitarz, Paweł Zalecki, Spectral metric and Einstein functionals for the Hodge–Dirac operator. J. Noncommut. Geom. (2024), published online first

DOI 10.4171/JNCG/573