In mathematics, the Thurston boundary of Teichmüller space of a surface is obtained as the boundary of its closure in the projective space of functionals on simple closed curves on the surface. The Thurston boundary can be interpreted as the space of projective measured foliations on the surface.
The Thurston boundary of the Teichmüller space of a closed surface of genus is homeomorphic to a sphere of dimension . The action of the mapping class group on the Teichmüller space extends continuously over the union with the boundary.
In mathematics, the Thurstonboundary of Teichmüller space of a surface is obtained as the boundary of its closure in the projective space of functionals...
In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure...
Poincaré conjecture (see the Solution of the Poincaré conjecture). William Thurston's geometrization program, formulated in the 1970s, provided a far-reaching...
the Thurston conjecture. One form of Thurston's geometrization theorem states: If M is a compact irreducible atoroidal Haken manifold whose boundary has...
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose...
{\displaystyle 3g-3+k} . The action extends to the Thurstonboundary of Teichmüller space, and the Nielsen-Thurston classification of mapping classes can be seen...
suppose that the sequences gi, hi converge to points μ,μ′ in the Thurstonboundary of Teichmüller space of projective measured laminations. If the points...
County, and Thurston County. In Tennessee, the boundaries are not used to control growth per se, but rather to define long-term city boundaries. (This was...
the Thurstonboundary, the Teichmüller geodesic ray associated to a flat surface does not always converge to the corresponding point on the boundary, though...
sum of projective planes. A classification of 3-manifolds results from Thurston's geometrization conjecture, proven by Grigori Perelman in 2003. More specifically...
started in Thurston's Princeton lecture notes. Hatcher also showed that irreducible, boundary-irreducible 3-manifolds with toral boundary have at most...
(not necessarily connected) surface that is compact and without boundary. The Thurston norm of c {\displaystyle c} is then defined to be ‖ c ‖ T = min...
geometric topology: for example as boundary points of the Teichmüller space (every point in the Thurstonboundary of the Teichmüller space is represented...
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