Dual Teichm\" uller spaces
dg-ga
2008-02-03 v3 High Energy Physics - Theory
Differential Geometry
Abstract
We describe in elementary geometrical terms Teichm\" uller spaces of decorated and holed surfaces. We construct explicit global coordinates on them as well as on the spaces of measured laminations with compact and closed support respectively. We show explicitly that the latter spaces are asymptotically isomorphic to the former. We discuss briefly quantisation of Teichm\" uller spaces and some other application of the constructed approach. The paper does not require any preliminary knowledge of the subject above the Poincar\' e uniformisation theorem.
Cite
@article{arxiv.dg-ga/9702018,
title = {Dual Teichm\" uller spaces},
author = {V. V. Fock},
journal= {arXiv preprint arXiv:dg-ga/9702018},
year = {2008}
}
Comments
LaTeX, 32 pages, 7 Postscript figures; more detailed discussion of quantization is added