Dual Teichm\" uller spaces
V.V.Fock (ITEP,Moscow)

TL;DR
This paper provides elementary geometric descriptions of Teichmüller spaces for decorated and holed surfaces, constructs explicit coordinates, and explores their asymptotic relationships and quantisation, accessible without prior advanced knowledge.
Contribution
It introduces explicit global coordinates for Teichmüller spaces and measured lamination spaces, and demonstrates their asymptotic isomorphism, with brief discussion on quantisation.
Findings
Explicit global coordinates on Teichmüller spaces
Asymptotic isomorphism between lamination and Teichmüller spaces
Discussion on quantisation of Teichmüller spaces
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Advanced Numerical Analysis Techniques
