Geometry of the Smallest 1-form Laplacian Eigenvalue on Hyperbolic Manifolds

We relate small 1-form Laplacian eigenvalues to relative cycle complexity on closed hyperbolic manifolds: small eigenvalues correspond to closed geodesics no multiple of which bounds a surface of small genus. We describe potential applications of this equivalence principle toward proving optimal torsion homology growth in families of hyperbolic 3-manifolds Benjamini–Schramm converging to H³.

Duke Scholars

Author Mark A. Stern Mathematics