A glimpse into Thurston’s work. (English) Zbl 1479.57040
Ohshika, Ken’ichi (ed.) et al., In the tradition of Thurston. Geometry and topology. Cham: Springer. 1-58 (2020).
Summary: We present an overview of some significant results of Thurston and their impact on mathematics.
For the entire collection see [Zbl 1470.57002].
For the entire collection see [Zbl 1470.57002].
MSC:
| 57K30 | General topology of 3-manifolds |
| 57M50 | General geometric structures on low-dimensional manifolds |
| 57-02 | Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes |
| 57-03 | History of manifolds and cell complexes |
| 01A60 | History of mathematics in the 20th century |
| 01A70 | Biographies, obituaries, personalia, bibliographies |
| 20F34 | Fundamental groups and their automorphisms (group-theoretic aspects) |
| 20F65 | Geometric group theory |
| 22E40 | Discrete subgroups of Lie groups |
| 30F20 | Classification theory of Riemann surfaces |
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 30F60 | Teichmüller theory for Riemann surfaces |
| 30F45 | Conformal metrics (hyperbolic, Poincaré, distance functions) |
| 37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
| 57K10 | Knot theory |
| 57R30 | Foliations in differential topology; geometric theory |
| 53A40 | Other special differential geometries |
| 58D05 | Groups of diffeomorphisms and homeomorphisms as manifolds |
| 00A30 | Philosophy of mathematics |
| 20F10 | Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) |
| 68Q70 | Algebraic theory of languages and automata |
| 57M05 | Fundamental group, presentations, free differential calculus |
| 57M07 | Topological methods in group theory |
| 57Q15 | Triangulating manifolds |
| 58A10 | Differential forms in global analysis |
Keywords:
foliation; contact structure; symplectic structure; conformal geometry; holomorphic motion; Kleinian groups; circle packing; automatic groups; tiling; mapping class groups; Teichmüller space; fashion design; linkage; anti-de Sitter geometry; higher Teichmüller theory; Grothendieck-Thurston theory; asymmetric metric; Schwarzian derivative; computer science; Ehrenpreis conjecture; transitional geometry; 3-manifolds; geometric structures; \((G, X)\)-structures; Dehn surgery; hyperbolic geometry; Thurston norm; Smith conjecture; Cannon-Thurston map; discrete conformal geometry; discrete Riemann mapping theoremReferences:
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