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Spectral Metric and Einstein Functionals for Hodge-Dirac operator

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arxiv 2307.14877 v3 pith:J5DLTPZ7 submitted 2023-07-27 math.DG math-phmath.MPmath.QAmath.SP

Ludwik Dąbrowski , Pawe{l} Zalecki , Andrzej Sitarz This is my paper · ORCID
classification math.DGmath-phmath.MPmath.QAmath.SP
keywords functionalsoperatoreinsteinhodge-diracmanifoldmetricspectralassociated
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abstract

We examine the metric and Einstein bilinear functionals of differential forms introduced in Adv.Math.,Vol.427,(2023)1091286, for Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. We show that they reproduce these functionals for the canonical Dirac operator on a spin manifold up to a numerical factor. Furthermore, we demonstrate that the associated spectral triple is spectrally closed, which implies that it is torsion-free.

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