Notes on notes of Thurston. (English) Zbl 0612.57009

Canary, R. D.; Epstein, D. B. A.; Green, P.

Analytical and geometric aspects of hyperbolic space, Symp. Warwick and Durham/Engl. 1984, Lond. Math. Soc. Lect. Note Ser. 111, 3-92 (1987).

[For the entire collection see Zbl 0601.00008.]
W. Thurston’s notes, ”The geometry and topology of 3-manifolds”, are of fundamental importance for all current research in low-dimensional topoloy. As class notes, they are often sketchy and are occasionally obscure. The authors have prepared a careful and detailed exposition of certain important portions of those notes, particularly of important topics in section 8 of those notes. For example, they treat the developing map, convexity, the deformation space, thickenings, the thick- thin decomposition, geometric and algebraic convergence, geodesic laminations and pleated surfaces.

Reviewer: J.W.Cannon

MSC:

57N10	Topology of general \(3\)-manifolds (MSC2010)
51M10	Hyperbolic and elliptic geometries (general) and generalizations
30F40	Kleinian groups (aspects of compact Riemann surfaces and uniformization)

Keywords:

hyperbolic manifold; Kleinian group; developing map; convexity; deformation space; thickenings; thick-thin decomposition; geodesic laminations; pleated surfaces

Citations:

Zbl 0601.00008