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math.GTDec 11, 2006
30
citations (OpenAlex)
authors
  • Ian Agol
arXiv abstractPDF
paper

Systoles of hyperbolic 4-manifolds

arXiv:math/0612290

Abstract

We prove that for any \e>0, there exists a closed hyperbolic 4-manifold with a closed geodesic of length < \e.

4 pages, 1 figure

Cited by in corpus (14)

  • Hyperbolic compactification of M-theory and de Sitter quantum gravity
  • NonLERFness of arithmetic hyperbolic manifold groups and mixed 3-manifold groups
  • Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups
  • Hyperbolic four-manifolds
  • Geodesics, volumes and Lehmer's conjecture
  • Trace fields and commensurability of link complements
  • Cusps and Commensurability Classes of Hyperbolic 4-Manifolds
  • Superrigidity, arithmeticity, normal subgroups: results, ramifications and directions
  • Prescribed virtual homological torsion of 3-manifolds
  • Length and stable length
  • Subspace stabilisers in hyperbolic lattices
  • The normal growth exponent of a codimension-1 hypersurface of a negatively curved manifold
  • Margulis numbers and number fields
  • Essential minimal volume of Einstein 4-manifolds
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