Download Acerca de la Geometría de Lobachevski by A. S. Smogorzhevski PDF

By A. S. Smogorzhevski

Show description

Read or Download Acerca de la Geometría de Lobachevski PDF

Similar geometry and topology books

L²-invariants: theory and applications to geometry and K-theory

In algebraic topology a few classical invariants - reminiscent of Betti numbers and Reidemeister torsion - are outlined for compact areas and finite team activities. they are often generalized utilizing von Neumann algebras and their lines, and utilized additionally to non-compact areas and countless teams. those new L2-invariants include very fascinating and novel info and will be utilized to difficulties coming up in topology, K-Theory, differential geometry, non-commutative geometry and spectral thought.

Extra info for Acerca de la Geometría de Lobachevski

Example text

The preimage of a path component of G\(Xn − Xn−1 ). The closure of an equivariant open n-dimensional cell is called an equivariant closed n-dimensional cell . 25, then the equivariant closed n-dimensional cells are just the G-subspaces Qi (G/Hi × Dn ). If X is a G-CW -complex, then G\X is a CW -complex. If G is discrete or if G is a Lie group and H ⊂ G is compact, then the H-fixed point set X H inherits a WH-CW -complex structure. Here and in the sequel NH = {g ∈ G | gHg −1 = H} is the normalizer of H in G and WH denotes the Weyl group NH/H of H in G.

Let βp be the number of p-cells in X. Then Tf n has a CW -structure with βp + βp−1 cells of dimension p. Hence the von Neumann dimension of the cellular Hilbert N (Gn )-chain module Cp (Tf n ) is βp + βp−1 . 12 (2) that (2) bp (Tf n ) ≤ βp + βp−1 . We have shown 0 ≤ b(2) p (Tf ) ≤ βp + βp−1 . n Since βp + βp−1 is independent of n, the claim follows by taking the limit for n → ∞. e. 2 on page 53]). This is a weaker notion than the notion of a (locally trivial) fiber bundle with typical fiber F [269, chapter 4, section 5].

J∈J A directed set I is a non-empty set with a partial ordering ≤ such that for two elements i0 and i1 there exists an element i with i0 ≤ i and i1 ≤ i. A net 18 1. L2 -Betti Numbers (xi )i∈I in a topological space is a map from a directed set to the topological space. The net (xi )i∈I converges to x if for any neighborhood U of x there is an index i(U ) ∈ I such that xi ∈ U for each i ∈ I with i(U ) ≤ i. A net (fi )i∈I in B(H) converges strongly to f ∈ B(H) if for any v ∈ H the net (fi (v))i∈I converges to f (v) in H.

Download PDF sample

Rated 4.87 of 5 – based on 3 votes