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The geometry of ideal 2-dimensional simplicial complexes

Published online by Cambridge University Press:  04 June 2001

Charalampos Charitos  and
Athanase Papadopoulos
Charalampos Charitos
Affiliation:
Agricultural University of Athens, Department of Mathematics, 75 Iera Odos, 11855 Athens, Greece e-mail:gmatxax@auadec.aua.gr
Athanase Papadopoulos
Affiliation:
Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7, rue René Descartes, 67084 Strasbourg, France e-mail:papadopoulos@math.u-strasbg.fr
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In this paper, we study geometric structures on 2-dimensional simplicial complexes. In particular, we consider hyperbolic structures and measured foliations on these simplicial complexes. We describe the spaces of such structures and we relate the two resulting spaces in a manner which is analogous to Thurston's compactification of the Teichmüller space of a surface.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 1 , January 2001 , pp. 39 - 66
Copyright
2001 Glasgow Mathematical Journal Trust