Algebraic topology. Errata (web draft, Nov. 2004) - download pdf or read online

By Hatcher A.

Show description

Read Online or Download Algebraic topology. Errata (web draft, Nov. 2004) PDF

Similar geometry and topology books

Download PDF by C.J.A. Evelyn, etc.: The seven circles theorem and other new theorems

Evelyn, Money-Coutts, Tyrrell. The seven circles theorem and different theorems (1974)(ISBN 095033040X)(75s)_MD_

Extra resources for Algebraic topology. Errata (web draft, Nov. 2004)

Sample text

15 A compact complex manifold M is Kobayashi hyperbolic iff every holomorphic map f : C → M is constant. Cf. [La, III, §2]. For example, if M is covered by a bounded domain in Cn , then it is Kobayashi hyperbolic. 16 Any holomorphic map between complex manifolds is distance non-increasing for the Kobayashi metric. 17 (Royden) The Teichm¨ uller metric on Teich(S) coincides with the Kobayashi metric. 18 Any holomorphic map f : Teich(S) → Teich(S) satisfies d(f X, f Y ) ≤ d(X, Y ) in the Teichm¨ uller metric.

This is the current [γ] associated to a closed loop. (ii) A positive weighted sum of closed curves Ci γi determines a current Ci [γi ]. For simplicity we suppressed the brackets in the future. Integral geometry. The integral geometric measure on G is defined as follows. Fix an oriented geodesic γ ⊂ H. Then there is an injective map γ × S 1 → G sending (x, θ) to the unique unoriented geodesic δ(x, θ) through x making angle θ with γ. ) The measure µ = (1/2) sin θdθ dx can be shown to be independent of the choice of chart.

1. There is a lift of f to a map H → H that extends to the identity on R. 2. The map f is homotopic to the identity rel ideal boundary. 3. The map f is isotopic to the identity rel ideal boundary, through uniformly quasiconformal maps. See [EaM]. A Riemann surface marked by X is a pair (Y, g) where g : X → Y is a quasiconformal map. Two marked Riemann surfaces (Y, g) and (Z, h) are equivalent if there is a conformal isomorphism α : Y → Z such that f = h−1 ◦ α ◦ g : X → X is isotopic to the identity rel ideal boundary.

Download PDF sample

Algebraic topology. Errata (web draft, Nov. 2004) by Hatcher A.


by Jeff
4.3

Rated 4.99 of 5 – based on 38 votes