Geometrische Topologie, Dynamik und das Werk von William P. Thurston. (German) Zbl 0543.57004

Reitberger, H.

Jahrb. Überblicke Math. 1984, Math. Surv. 17, 221-227 (1984).

[For the entire collection see Zbl 0535.00005.]
A survey of the work of Thurston, illustrated by comparisons with the theory of surfaces. The author complains rightly that most of the recent works of Thurston is not in the public domain and therefore not open to public scrutiny in an area that abounds with wrong proofs (Dehn’s Lemma!), wrong counterexamples (Whitehead), etc.

Reviewer: H.Guggenheimer

MSC:

57-03	History of manifolds and cell complexes
01A65	Development of contemporary mathematics
57N10	Topology of general \(3\)-manifolds (MSC2010)
57N05	Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57R50	Differential topological aspects of diffeomorphisms
37D99	Dynamical systems with hyperbolic behavior
57R30	Foliations in differential topology; geometric theory
30F40	Kleinian groups (aspects of compact Riemann surfaces and uniformization)

Keywords:

diffeomorphisms of surfaces; Pseudo-Anosov diffeomorphisms; hyperbolicity of atoroidal 3-manifolds; dynamics of Kleinian groups. Thurston, W. P; theory of surfaces; Dehn’s Lemma