Spectral forms and de-Rham Hodge operator

2024/10/11 by Jian Wang, Yong Wang, Wang, Jian +3 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.08506

openalex publication_date 2024/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The noncommutative residue, divergence theorems and the spectral geometry functional
• The spectral torsion for the one form rescaled Dirac operator
• On geometric spectral functionals

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