By A. H. Assadi, P. Vogel (auth.), Andrew Ranicki, Norman Levitt, Frank Quinn (eds.)

Show description

Read or Download Algebraic and Geometric Topology: Proceedings of a Conference held at Rutgers University, New Brunswick, USA July 6–13, 1983 PDF

Similar geometry and topology books

Complex Functions Examples c-2 - Analytic Functions

This is often the second one textbook you could obtain at no cost containing examples from the idea of advanced services. there'll even be examples of complicated features, complicated limits and complicated line integrals.

Extra resources for Algebraic and Geometric Topology: Proceedings of a Conference held at Rutgers University, New Brunswick, USA July 6–13, 1983

Sample text

First, pass to a subsequence such that ψ n (ui ) → vi ∈ X. Next, choose a chain of overlapping rectangles connecting v1 to v2 . In case v1 or v2 is a zero of q, choose the initial or terminal rectangle so it also contains ψ n (ui ) for infinitely many n. Let U1 , . . , Um be open sets in the overlap of adjacent rectangles. Then by the lemma above, we can find yj ∈ Uj and xj ∈ E such that ψ n (xj ) → yj along a further subsequence. 61, v1 is generic for the same measure as y1 . Similarly yi and yi+1 are generic for the same measure, as are ym and v2 .

Note that F : X → X, while locally affine, is not Anosov — it preserves a splitting of the tangent space, but the splitting is not along the stable and unstable manifolds of F . 12 Bers embedding In this section we discuss the Teichm¨ uller space of a quite general Riemann surface X, and its embedding as a domain in a complex Banach space. Ideal boundary. Let X = H/ΓX be a hyperbolic Riemann surface, presented as the quotient of the upper halfplane by a Fuchsian group. We do not assume that X has finite volume.

62 Given a sequence N ⊂ N and a nonempty open set U ⊂ X, there is an x ∈ Ei and a further subsequence N ′ ⊂ N along which ψ n (x) → y ∈ U . Proof. Let K ⊂ U be a compact set of positive measure, and let Kn = ψ −n (K). Then since ψ is measure preserving, the sum over n ∈ N of the |q|-measure of Kn diverges, and thus (by Borel-Cantelli) there is a set of A ⊂ E of positive Lebesgue measure consisting of points with ψ n (x) ∈ K for infinitely many n ∈ A. Passing to a convergent subsequence yields the lemma.

Download PDF sample

Algebraic and Geometric Topology: Proceedings of a by A. H. Assadi, P. Vogel (auth.), Andrew Ranicki, Norman
Rated 4.64 of 5 – based on 5 votes