Near optimal spectral gaps for line bundles on hyperbolic three-manifolds

Michael Magee; Anna Roig-Sanchis; Joe Thomas

Near optimal spectral gaps for line bundles on hyperbolic three-manifolds

Group Theory 2026-08-01 v1 Operator Algebras Probability Representation Theory Spectral Theory

Authors: Michael Magee , Anna Roig-Sanchis , Joe Thomas

Abstract

We prove that there exists a sequence of two-torsion Hermitian line bundles on closed hyperbolic three-manifolds, with volume tending to infinity, and with asymptotically optimal smallest eigenvalue of the Laplacian. The proof stems from recent advances in the program of strongly convergent unitary representations of discrete groups.

Keywords

spectral gaps line bundles hyperbolic three-manifolds Laplacian unitary representations

Cite

@article{arxiv.2608.00386,
  title  = {Near optimal spectral gaps for line bundles on hyperbolic three-manifolds},
  author = {Michael Magee and Anna Roig-Sanchis and Joe Thomas},
  journal= {arXiv preprint arXiv:2608.00386},
  year   = {2026}
}