Event

Talk
Dirac isospectrality of lens spaces
Sebastian Boldt (HU Berlin)
21 Jun 2016, 17:00 – 18:00

To what extent are lens spaces determined by the spectrum of their Dirac operator(s)? The Dirac spectrum of the sphere is very well known. When passing to lens spaces, the eigenvalues remain the same but the multiplicities are in general smaller. We present two approaches to describe the latter. In the first approach, we encode the multiplicities into power series. These turn out to represent meromorphic functions. An analysis of their poles then leads to a partial rigidity result in dimension three. In the second approach we associate with each lens space an affine lattice. The multiplicities of the Dirac operator on a lens space are then connected to the number of points in the associated lattice with a certain 1-norm by a concrete formula. As a consequence we obtain a finite Dirac isospectrality criterion for lens spaces which in turn leads to several infinite families of Dirac isospectral pairs. We complement these with computer generated isospectral pairs and conclude with some unexpected phenomena.

Related to:

• Sebastian Boldt
• [C2] Differential Geometry: Geometric and Spectral Invariants of Riemannian, Lorentzian and conformal manifolds