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 $\mathbb{H}^3.$ 
Michael Lipnowski, Mark Stern
math.GT math.DG math.NT