Abstract
As we have learned in Sect. 1.6 a given spectral triple \((\mathscr {A,H,D})\) ought to be considered as a representative of the entire family of triples \((\mathscr {A},\mathscr {H},\mathscr {D}_{\mathbb {A}})\), which yield equivalent geometries. It is therefore of utmost importance to understand how the spectral action is affected by the fluctuations of geometry. We explore the meromorphic structure of the fluctuated zeta function and, for regular spectral triples with simple dimension spectra, we provide a few formulae for the noncommutative integrals. Finally, we sketch the method of operator perturbations.
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