Spectral Metric and Einstein Functionals for Hodge-Dirac operator

Andrzej Sitarz; Ludwik D\k{a}browski; Pawe{\l} Zalecki

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

Spectral Metric and Einstein Functionals for Hodge-Dirac operator

Ludwik D\k{a}browski , Pawe{\l} Zalecki , Andrzej Sitarz This is my paper

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keywords functionalsoperatoreinsteinhodge-diracmanifoldmetricspectralassociated

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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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On Geometric Spectral Functionals
math-ph 2025-05 unverdicted novelty 6.0

Spectral functionals via Wodzicki residue recover geometric tensors including volume, metric, curvature and torsion on manifolds with torsion and yield chiral invariants.