Decorated Teichmüller theory of bordered surfaces
نویسندگان
چکیده
منابع مشابه
Teichmüller Theory of Bordered Surfaces
We propose the graph description of Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces). Introducing new parameters, we formulate this theory in terms of hyperbolic geometry. We can then describe both classical and quantum theories having the proper number of Thurston variables (foliation-shear coordinates), mapping-class group invariance (both classical...
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This survey covers earlier work of the author as well as recent work on Riemann's moduli space, its canonical cell decomposition and compactification, and the related operadic structure of arc complexes.
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We define a category Fat whose objects are isomorphism classes of bordered fat graphs and show that its geometric realization is a classifying space for the bordered mapping class groups. We then construct a CW structure on this geometric realization with one cell per isomorphism classes of bordered fat graphs. Its cellular cochain complex gives a bordered graph complex which computes the integ...
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The clique graph K(G) of a graph G is the intersection graph of all its (maximal) cliques. A graph G is said to be K-divergent if the sequence of orders of its iterated clique graphs |Kn(G)| tends to infinity with n, otherwise it is K-convergent. K-divergence is not known to be computable and there is even a graph on 8 vertices whose K-behaviour is unknown. It has been shown that a regular Whit...
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We construct geometric models for cluster algebras associated with bordered surfaces with marked points, for any choice of coefficients of geometric type, using generalized decorated Teichmüller spaces. In this context, the cluster variables are interpreted as suitably renormalized lambda lengths.
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2004
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2004.v12.n4.a2