Spectral metric and Einstein functionals for the Hodge–Dirac operator
Ludwik Dąbrowski
SISSA (Scuola Internazionale Superiore di Studi Avanzati), Trieste, ItalyAndrzej Sitarz
Jagiellonian University, Kraków, PolandPaweł Zalecki
Jagiellonian University, Kraków, Poland
![Spectral metric and Einstein functionals for the Hodge–Dirac operator cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-jncg.png&w=3840&q=90)
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