Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1896904 | Journal of Geometry and Physics | 2008 | 14 Pages |
Abstract
To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose “Riemannian” aspect (Hilbert space and Dirac operator) encode the boundary action through its Patterson–Sullivan measure. We prove that the ergodic rigidity theorem for this boundary action implies that the zeta functions of the spectral triple suffice to characterize the (anti-)complex isomorphism class of the corresponding Riemann surface. Thus, you can hear the complex analytic shape of a Riemann surface, by listening to a suitable spectral triple.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Gunther Cornelissen, Matilde Marcolli,