Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds
Geometric Topology
2016-11-14 v1 Differential Geometry
Number Theory
Abstract
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
Keywords
Cite
@article{arxiv.1611.03574,
title = {Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds},
author = {Michael Lipnowski and Mark Stern},
journal= {arXiv preprint arXiv:1611.03574},
year = {2016}
}