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Introduction to Thurston's theorems
Multi angle
Authors : Hubbard, John H. (Author of the conference)
CIRM (Publisher )
30F40 - Kleinian groups, See also {20H10}
30F60 - Teichmüller theory
32G05 - Deformations of complex structures
37F35 - Conformal densities and Hausdorff dimension
37F45 37F40 - Geometric limits in holomorphic dynamics
CIRM (Publisher )
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Abstract :
W. Thurston's theorems almost all aim to give a purely topological problem an appropriate geometry, or to identify an appropriate obstruction.. We will illustrate this in two examples:
--The Thurston pullback map to make a rational map from a post-critically finite branched cover of the sphere, and
--The skinning lemma, to find a hyperbolic structure for a Haken 3-manifold.
In both cases, either the relevant map on Teichmüller space has a fixed point, solving the geometrization problem, or there is an obstruction consisting a multicurve.
Keywords : Teichmüller theory; Thurston pull-back map; Skinning lemma
MSC Codes : --The Thurston pullback map to make a rational map from a post-critically finite branched cover of the sphere, and
--The skinning lemma, to find a hyperbolic structure for a Haken 3-manifold.
In both cases, either the relevant map on Teichmüller space has a fixed point, solving the geometrization problem, or there is an obstruction consisting a multicurve.
Keywords : Teichmüller theory; Thurston pull-back map; Skinning lemma
30F40 - Kleinian groups, See also {20H10}
30F60 - Teichmüller theory
32G05 - Deformations of complex structures
37F35 - Conformal densities and Hausdorff dimension
37F45 37F40 - Geometric limits in holomorphic dynamics
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/11/2021 Conference Date : 20/09/2021 Subseries : Research School arXiv category : Dynamical Systems ; Electrical Engineering and Systems Science Mathematical Area(s) : Dynamical Systems & ODE ; Topology Format : MP4 (.mp4) - HD Video Time : 00:59:25 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-20_Hubbard.mp4 
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Information on the Event
Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeEvent Organizers : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk Dates : 20/09/2021 - 24/09/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2546.html
Citation Data
DOI : 10.24350/CIRM.V.19812603Cite this video as: Hubbard, John H. (2021). Introduction to Thurston's theorems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19812603 URI : http://dx.doi.org/10.24350/CIRM.V.19812603 |
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Bibliography
- Hubbard, Teichmüller theory vols 1-4, Matrix editions -
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