2003/06/26 by Athanase Papadopoulos, Papadopoulos, Athanase, Robert Penner +2
Mathematics · #30F60 #32G15 #57M10 #57M50 #57R30 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.GT #msc:30F60 #msc:32G15 #msc:57M10 #msc:57M50 #msc:57R30
paper · pdf · doi:10.48550/arxiv.math/0306370
24 pages, 7 figures
arxiv created 2003/06/26 · openalex publication_date 2003/06/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The space of broken hyperbolic structures generalizes the Teichmüller space of a punctured surface, and the space of projectivized broken measured foliations (equivalently, the space of projectivized affine foliations) generalizes the space of projectivized measured foliations. Just as projectivized measured foliations provide Thurston's boundary for Teichmüller space, so too do projectivized broken measured foliations form a boundary for the space of broken hyperbolic structures. In this paper, we naturally extend the Weil-Petersson Kähler two-form and the Thurston symplectic form to their broken analogues and prove that the former suitably limits to the latter. The proof in sketch follows earlier work of the authors for measured foliations and depends upon techniques from decorated Teichmüller theory, which is also applied here to a further study of broken hyperbolic structures.