2012/10/19 by Julien Roger, Roger, Julien
Mathematics · #32G15 #57M50 #57M60 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1210.5509
openalex publication_date 2012/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We start by describing how ideal triangulations on a surface degenerate under pinching of a multicurve. We use this process to construct a homomorphism from the Ptolemy groupoid of a surface to that of a pinched surface which is natural with respect to the action of the mapping class group. We then apply this construction to the study of shear coordinates and their extension to the augmented Teichmüller space. In particular, we give an explicit description of the action of the mapping class group on the augmented Teichmüller space in terms of shear coordinates.