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


Journal Article

© 2018, Springer Nature Switzerland AG. 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 H 3 .

Full Text

Duke Authors

Cited Authors

  • Lipnowski, M; Stern, M

Published Date

  • December 1, 2018

Published In

Volume / Issue

  • 28 / 6

Start / End Page

  • 1717 - 1755

International Standard Serial Number (ISSN)

  • 1016-443X

Digital Object Identifier (DOI)

  • 10.1007/s00039-018-0471-x

Citation Source

  • Scopus