Riemann surfaces with boundary and natural triangulations of the Teichmüller space
Gabriele Mondello (2011)
Journal of the European Mathematical Society
Similarity:
We compare some natural triangulations of the Teichmüller space of hyperbolic surfaces with geodesic boundary and of some bordifications. We adapt Scannell–Wolf’s proof to show that grafting semi-infinite cylinders at the ends of hyperbolic surfaces with fixed boundary lengths is a homeomorphism. This way, we construct a family of equivariant triangulations of the Teichmüller space of punctured surfaces that interpolates between Bowditch–Epstein–Penner’s (using the spine construction)...