Spectral forms and de-Rham Hodge operator

Jian Wang; Yong Wang; Mingyu Liu

doi:10.1016/j.geomphys.2025.105535

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arXiv · 2410.08506

Spectral forms and de-Rham Hodge operator

Jian Wang·Yong Wang·Mingyu Liu

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Abstract

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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Jian Wang, Yong Wang, Mingyu Liu. 2024-10-11. Spectral forms and de-Rham Hodge operator. https://doi.org/10.1016/j.geomphys.2025.105535

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