Dual Teichm\" uller spaces

Details Dual Teichm\" uller spaces Dual Teichm\" uller spaces

1997-02-20

arxiv.org/abs/dg-ga/9702018v3

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 32 pages, 7 Postscript figures; more detailed discussion of quantization is added

Scientific paper

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.

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