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Spectral forms and de-Rham Hodge operator
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Spectral forms and de-Rham Hodge operator
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Motivated by the trilinear functional of differential one-forms, spectral triple and spectral torsion for the Hodge-Dirac operator, we introduce a multilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue, which generalize the spectral torsion defined by Dabrowski-Sitarz-Zalecki. The main results of this paper recover two forms, torsion of the linear connection and four forms by the noncommutative residue and perturbed de-Rham Hodge operators, and provides an explicit computation of generalized spectral torsion associated with the perturbed de-Rham Hodge Dirac triple.
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Cited by 1 Pith paper
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On Geometric Spectral Functionals
Spectral functionals via Wodzicki residue recover geometric tensors including volume, metric, curvature and torsion on manifolds with torsion and yield chiral invariants.
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