Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces
type: Dataset
description: We provide analogues for non-orientable surfaces with or without boundary or punctures of several basic theorems in the setting of the Thurston theory of surfaces which were developed so far only in the case of orientable surfaces. Namely, we provide natural analogues for non-orientable surfaces of the Fenchel-Nielsen theorem on the parametrization of the Teichmüller space of the surface, the Dehn-Thurston theorem on the parametrization of measured foliations in the surface, and the Hatcher-Thurston theorem, which gives a complete minimal set of moves between pair of pants decompositions of the surface. For the former two theorems, one in effect drops the twisting number for any curve in a pants decomposition which is 1-sided, and for the latter, new elementary moves on pants decompositions are introduced.
landing page: 1093-6106
keyword: 30f60--32g15--57m50--57n16
keyword: dehn-thurston-theorem
keyword: fenchel-nielsen-theorem
keyword: hatcher-thurston-theorem
keyword: infoeu-reposemanticsarticle
keyword: journal-articles
keyword: mathmath-gtmathematics-mathgeometric-topology-mathgt
keyword: non-orientable-surfaces
keyword: pants-decompositions
keyword: teichmu-ller-space
keyword: thurstons-boundary
issued: 2026-05-09T13:13:14.643799
modified: 2026-05-09T13:13:14.643804
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces
type: Distribution
format: HTML
access URL: https://hal.science/hal-00856638
issued: 2026-05-09T13:13:14.657127
modified: 2026-05-09T13:13:14.629262