3
$\begingroup$

Is there a good survey paper which discusses the common ways of building hyperbolic $n$-manifolds?

$\endgroup$
  • 2
    $\begingroup$ Section 3.1 here. $\endgroup$ – Misha Jan 5 at 13:15
  • 4
    $\begingroup$ See Dave Witte-Morris' book for arithmetic groups, and section 6.5 for the non-arithmetic Gromov-Piatetskii-Shapiro examples. deductivepress.ca These and variants (together with Selberg's Lemma) are essentially the only known general method for proving the existence of finite volume hyperbolic $n$-manifolds (variants are given here arxiv.org/abs/1802.04619). In 3 dimensions, in some sense the geometrization theorem gives a construction of all finite volume hyperbolic 3-manifolds. The Deligne-Mostow construction gives some examples as moduli spaces of polygons. $\endgroup$ – Ian Agol Jan 5 at 18:19
  • 2
    $\begingroup$ For recent constructions of finite volume hyperbolic manifolds with various properties, see: arxiv.org/abs/1008.2646 arxiv.org/abs/1507.02747 arxiv.org/abs/1703.10561 arxiv.org/abs/1812.06536 arxiv.org/abs/1904.12720 $\endgroup$ – Ian Agol Jan 5 at 18:21
5
$\begingroup$

Not a paper, but a book : Foundations of Hyperbolic Manifolds by John Ratcliffe. Chapters 10 and 11 might contain what you're looking for. Also available here.

Concerning 4-manifolds, you have a survey by Bruno Martelli here.

Also, I'm sure you can find what you want typing construction of hyperbolic manifolds on your favorite search engine.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.