A Picard horn, also called the Picard topology or Picard model, is one of the oldest known hyperbolic 3-manifolds, first described by Émile Picard[1] in 1884.[2] The manifold is the quotient of the upper half-plane model of hyperbolic 3-space by the projective special linear group, . It was proposed as a model for the shape of the universe in 2004.[3] The term "horn" is due to pseudosphere models of hyperbolic space.
![{\displaystyle \operatorname {PSL} _{2}(\mathbf {Z} [i])}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5f6f313b6977b5c3b269fd159ea92c7f219133f)
- ^ "Émile Picard - Académie des sciences". Archived from the original on 2012-03-30. Retrieved 2011-09-26.
- ^ Émile Picard (1884-03-07). "Sur un groupe de transformations des points de l'espace situés du même côté d'un plan". Bulletin de la Société Mathématique de France (in French). 12: 43–47. Retrieved 2011-08-24.
- ^ Cite error: The named reference
Aurich0403597was invoked but never defined (see the help page).