On the geometry and dynamics of diffeomorphisms of surfaces.

*(English)*Zbl 0674.57008The preprint version of this paper had appeared about 1976. Now, after twelve years, it is published. Twelve years ago it was a research announcement, now it is a classic. The theory announced in it was exposed in the Proceedings of a seminar at Orsay [cf. A. Fathi, F. Laudenbach, V. Poenaru et al., Travaux de Thurston sur les surfaces, Asterisque 66-67 (1979; Zbl 0446.57005 ff.)] and was used and extended by many mathematicians. Recently an introduction for beginners has appeared: A. J. Casson and S. A. Bleiler, Automorphisms of surfaces after Nielsen and Thurston (1988; Zbl 0649.57008). I think that there is no need now to describe the contents of this paper in detail: the concept of a measured foliation, the classification of diffeomorphisms, the construction of a natural boundary of the Teichmüller space. Now all this is the core of two-dimensional topology and is known not only to experts. The exciting development inspired by these ideas is described in a preface added to the original preprint. This preface is accompained by a list of references to papers influenced by the reviewed one. This list is useful, but surely incomplete and not up to date, some papers listed as preprints are already published. Besides the addition of the preface and the bibliography, the original preprint remained unchanged.

Reviewer: N.Ivanov

##### MSC:

57N05 | Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010) |

57R50 | Differential topological aspects of diffeomorphisms |

37D99 | Dynamical systems with hyperbolic behavior |

57R52 | Isotopy in differential topology |

##### Keywords:

space of simple closed curves; geodesic lamination; pseudo Anosov diffeomorphism; measured foliation; classification of diffeomorphisms; boundary of the Teichmüller space
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\textit{W. P. Thurston}, Bull. Am. Math. Soc., New Ser. 19, No. 2, 417--431 (1988; Zbl 0674.57008)

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##### References:

[1] | Jakob Nielsen, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Math.-Phys. Medd. 21 (1944), no. 2, 89. · Zbl 0063.05952 |

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