Leafwise cohomological expression of dynamical zeta functions on foliated dynamical systems

Abstract

A Riemmanian foliated dynamical system of 3-dimension $({\mathrm{RFDS}}^3)$ is a closed Riemannian 3-manifold with additional structures: foliation, dynamical system. In the context of arithmetic topology, it is a geometric/analytic analogue of an arithmetic scheme with a conjectural dynamical system suggested by C. Deninger. In this paper, we show leafwise cohomological expression of dynamical zeta function on a Riemannian foliated dynamical system.

10 pages

References in corpus (2)

• Analogies between analysis on foliated spaces and arithmetic geometry
• Arithmetic Geometry and Analysis on Foliated Spaces