TY - JOUR
T1 - Broken hyperbolic structures and affine foliations on surfaces
AU - Oertel, Ulrich
AU - Papadopoulos, Athanase
PY - 2004/6/21
Y1 - 2004/6/21
N2 - 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.
AB - 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.
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U2 - 10.1016/S0019-3577(04)90019-5
DO - 10.1016/S0019-3577(04)90019-5
M3 - Article
AN - SCOPUS:4444377382
VL - 15
SP - 269
EP - 282
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
SN - 0019-3577
IS - 2
ER -