Automorphisms of Surfaces After Nielsen and Thurston
Cambridge University Press, 1988 - Mathematics - 104 pages
This book, which grew out of Steven Bleiler's lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology. In particular it provides a concise exposition of the work of Neilsen and Thurston on the automorphisms of surfaces. The reader requires only an understanding of basic topology and linear algebra, while the early chapters on hyperbolic geometry and geometric structures on surfaces can profitably be read by anyone with a knowledge of standard Euclidean geometry desiring to learn more abour other 'geometric structures'.
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Automorphisms of Surfaces after Nielsen and Thurston
Andrew J. Casson,Steven A. Bleiler
No preview available - 1988
1-submanifold angle automorphism axis boundary leaves called chart Choose circle closed curve closed orientable hyperbolic closure compact complete component Consider constructed contained continuous contracting converges core crown defined Definition denote dense direction disjoint union distance distinct edges element empty endpoints equal essential Euclidean Example Exercise exists extend Figure finite fixed points follows geodesic boundary geodesic lamination given hence homeomorphism homotopic ideal identity implies induces integer interior intersection interval invariant inversion isolated isometry isotopic lamination leaf Lemma lift line field liſt matrix measure meets metric minimal intersection neighborhood non-empty non-periodic Note Observe orientable hyperbolic surface Poincare disk polygon preimage preserving principal region Proof proved rectangle reflections Remark respectively restriction separate sequence shows sided singular stable subset Suppose surface F tangent Theorem translation transverse union unique universal cover usual vertices