Broken hyperbolic structures and affine foliations on surfaces

Ulrich Oertel, Athanase Papadopoulos

Research output: Contribution to journalArticlepeer-review

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Abstract

In this paper, we introduce two new kinds of structures on a non-compact surface: broken hyperbolic structures and broken measured foliations. The space of broken hyperbolic structures contains the Teichmüller space of the surface as a subspace. The space of broken measured foliations is naturally identified with the space of affine foliations of the surface. We describe a topology on the union of the space of broken hyperbolic structures and of the space of broken measured foliations which generalizes Thurston's compactification of Teichmüller space.

Original languageEnglish (US)
Pages (from-to)269-282
Number of pages14
JournalIndagationes Mathematicae
Volume15
Issue number2
DOIs
StatePublished - Jun 21 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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