Download Automorphisms of Surfaces after Nielsen and Thurston by Andrew J. Casson PDF

By Andrew J. Casson

This ebook, which grew out of Steven Bleiler's lecture notes from a path given by way of Andrew Casson on the college of Texas, is designed to function an creation to the purposes of hyperbolic geometry to low dimensional topology. particularly it offers a concise exposition of the paintings of Neilsen and Thurston at the automorphisms of surfaces. The reader calls for purely an knowing of simple topology and linear algebra, whereas the early chapters on hyperbolic geometry and geometric constructions on surfaces can profitably be learn via somebody with an information of ordinary Euclidean geometry meaning to research extra abour different 'geometric structures'.

Show description

Read Online or Download Automorphisms of Surfaces after Nielsen and Thurston PDF

Similar topology books

Boundedly Controlled Topology. Foundations of Algebraic Topology and Simple Homotopy Theory

A number of fresh investigations have centred recognition on areas and manifolds that are non-compact yet the place the issues studied have a few type of "control close to infinity". This monograph introduces the class of areas which are "boundedly managed" over the (usually non-compact) metric area Z. It units out to advance the algebraic and geometric instruments had to formulate and to turn out boundedly managed analogues of a number of the ordinary result of algebraic topology and straightforward homotopy concept.

Topology and Teichmuller Spaces: Katinkulta, Finland 24-28 July 1995

This court cases is a suite of articles on Topology and Teichmuller areas. distinct emphasis is being wear the common Teichmuller area, the topology of moduli of algebraic curves, the distance of representations of discrete teams, Kleinian teams and Dehn filling deformations, the geometry of Riemann surfaces, and a few comparable issues.

Why Prove it Again?: Alternative Proofs in Mathematical Practice

This monograph considers a number of recognized mathematical theorems and asks the query, “Why end up it back? ” whereas reading replacement proofs. It explores the various rationales mathematicians could have for pursuing and proposing new proofs of formerly validated effects, in addition to how they pass judgement on even if proofs of a given end result are varied.

Extra info for Automorphisms of Surfaces after Nielsen and Thurston

Sample text

Proof: 91 = {M t } is a basis of M\. 6, {U M} is therefore a basis of V M~?. Hence U M, = V M^and V ^ i s a principal filter. 4 Π M t < M i 0 for all indices i0; hence Π Mt ζζ. 6 {Μλ n ... n M„} is a basis of Mx A ... Λ Μ η , whence M1 n ... n M ^ = A/j" Λ ... Λ Μ^. I The following example shows that the inf of an infinity of principal filters need not be a principal filter: Let An be the set of natural numbers ^ n. Then H {^4W : ne N} = 0, hence Π ^4n = 0 = 0. However, the filter /\ An is the Fréchet-filter associated with the natural numbers (cf.

From S eUv and q e 6 , it follows that S eUQ and hence (U 3 ) is verified with U = V = S. 6 we see that rp = Uv defines a topology τ on R. From S e S and p e S we have S eUP , hence S G rp. T h u s S contains only r-open sets. On the other hand, let M be an arbitrary r-open set. 1, an Sv e S such thâtp G Sv and Sv c M. By (c) we likewise have M = U {Sv : p G M} e S This proves that 6 contains all possible τ-open sets. To prove the converse, let r be a topology on R. 3 the system 6 of all r-open sets possesses properties (a)-(c) and thus defines, in the manner pre­ viously shown, a topology τ' on R.

Since R contains all points, it also is closed. But Co = R and CR = & and both these sets must therefore also be open. , Mn be open sets and pe Μλη ... n Mn . Then pe Mv and (Definition 3a, FJ. , n. Therefore Mxn ... n Mnerp 2 A point p such that M e rp is also called inner point of M. A set is open if and only if all its points are inner points. 3 When we wish to emphasize the underlying topology r without which, of course, we could not define our new concepts, we speak of "τ-open" and "τ-closed" sets, etc.

Download PDF sample

Rated 4.05 of 5 – based on 38 votes

Author: admin