Ptolemy groupoids, shear coordinates and the augmented Teichmuller space
Geometric Topology
2013-05-31 v2
Abstract
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 Teichm\"uller space. In particular, we give an explicit description of the action of the mapping class group on the augmented Teichm\"uller space in terms of shear coordinates.
Cite
@article{arxiv.1210.5509,
title = {Ptolemy groupoids, shear coordinates and the augmented Teichmuller space},
author = {Julien Roger},
journal= {arXiv preprint arXiv:1210.5509},
year = {2013}
}
Comments
21 pages, 13 figures. v2: minor corrections, added the once-punctured torus as an example