Twisted Ruelle zeta function on hyperbolic manifolds and complex-valued analytic torsion

2020/04/25 by Polyxeni Spilioti, Spilioti, Polyxeni
Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Spectral Theory (math.SP) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2004.13474

openalex publication_date 2020/04/25 · openalex created_date 2023/05/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the twisted Ruelle zeta function associated with the geodesic flow of a compact, hyperbolic, odd-dimensional manifold X. The twisted Ruelle zeta function is associated with an acyclic representation χ\colon π₁(X) → \GL_n(\C), which is close enough to an acyclic, unitary representation. In this case, the twisted Ruelle zeta function is regular at zero and equals the square of the refined analytic torsion, as it is introduced by Braverman and Kappeler in \citeBK2, multiplied by an exponential, which involves the eta invariant of the even part of the odd-signature operator, associated with χ.

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