Book Review: Thurston’s work on surfaces

DOI10.1090/S0273-0979-2013-01419-8zbMath1275.00015MaRDI QIDQ2864926

Dan Margalit

Publication date: 27 November 2013

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Collections of articles of miscellaneous specific interest (00B15) General geometric structures on low-dimensional manifolds (57M50) Collected or selected works; reprintings or translations of classics (01A75) Teichmüller theory for Riemann surfaces (30F60) History of manifolds and cell complexes (57-03) External book reviews (00A17)

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Cites Work

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• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• The congruence subgroup problem for pure braid groups: Thurston's proof.
• On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus
• On the minimum dilatation of braids on punctured discs
• Small dilatation mapping classes coming from the simplest hyperbolic braid
• Closed surface bundles of least volume
• Random walks on the mapping class group
• Small dilatation pseudo-Anosov homeomorphisms and 3-manifolds
• Abelian and solvable subgroups of the mapping class group
• A family of pseudo-Anosov braids with small dilatation
• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Stretching factors of pseudo-Anosov homeomorphisms
• The asymptotic behavior of least pseudo-Anosov dilatations
• Research announcement: The structure of groups with a quasiconvex hierarchy.
• New proofs of some results of Nielsen
• The geometry of Teichmüller space via geodesic currents
• The Teichmüller geodesic flow
• The real analytic theory of Teichmüller space
• On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces
• Geodesic laminations from Nielsen's viewpoint
• Flow equivalence, hyperbolic systems and a new zeta function for flows
• An extremal problem for quasiconformal mappings and a theorem by Thurston
• Train-tracks for surface homeomorphisms
• End periodic surface homeomorphisms and 3-manifolds
• On the forcing relation for surface homeomorphisms
• Periodic points of Hamiltonian surface diffeomorphisms
• Normal all pseudo-Anosov subgroups of mapping class groups
• Analytic foliations and the theory of levels
• Fixed points of pseudo-Anosov diffeomorphisms of surfaces
• On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number
• Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms
• An Implementation of the Bestvina–Handel Algorithm for Surface Homeomorphisms
• Polynomial invariants for fibered 3-manifolds and Teichmüller geodesics for foliations
• Ideal triangulations of pseudo-Anosov mapping tori
• A recipe for short-word pseudo-Anosovs
• A transcendental invariant of pseudo-Anosov maps
• Entropy in Dimension One
• Échanges d'intervalles et transformations induites
• Bounds on Least Dilatations
• A Construction of Pseudo-Anosov Homeomorphisms
• The lower central series and pseudo-Anosov dilatations
• The Minimum Dilatation of Pseudo-Anosov 5-Braids
• The Minimal Dilatation of a Genus-Two Surface
• On period minimal pseudo-Anosov braids
• Transitivity of surface dynamics lifted to Abelian covers
• Global shadowing of pseudo-Anosov homeomorphisms
• Ergodic Actions of the Mapping Class Group
• A "Tits-Alternative" for Subgroups of Surface Mapping Class Groups
• Growth rate of surface homeomorphisms and flow equivalence
• On the geometry and dynamics of diffeomorphisms of surfaces
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Smooth models of Thurston's pseudo-Anosov maps
• Examples of Pseudo-Anosov Homeomorphisms
• An Upper Bound for the Least Dilatation
• Periodic orbits of period 3 in the disc
• The forcing partial order on the three times punctured disk
• Démonstration d'un théorème de Penner sur la composition des twists de Dehn
• A Note on Pseudo-Anosov Maps with Small Growth Rate
• Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents
• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. III