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

February 23, 2017 | Geometry And Topology | By admin | 0 Comments

By A. S. Smogorzhevski

Show description

Read Online or Download Acerca de la Geometría de Lobachevski PDF

Similar geometry and topology books

The seven circles theorem and other new theorems

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

New Scientific Applications of Geometry and Topology (Proceedings of Symposia in Applied Mathematics, V. 45)

Geometry and topology are matters commonly thought of to be "pure" arithmetic. lately, even though, a number of the tools and leads to those parts have stumbled on new software in either wet-lab technology (biology and chemistry) and theoretical physics. Conversely, technological know-how is influencing arithmetic, from posing questions that decision for the development of mathematical types to exporting theoretical equipment of assault on long-standing difficulties of mathematical curiosity.

Extra info for Acerca de la Geometría de Lobachevski

Example text

L Exanple 2 . Let h" denote the set of polyhomeomorphians of E^ onto itself having compact support . The hypothesis of compact support enables us to define on H^ , as above , both a function ^ace polystructure and a linear polystructure , Let H^ , H^ be the resulting topological spaces, both having H^ as underlying set . Then it appears that H^ , H^ have different homotopy structures . By Alexander's Lemma on isotopy , it is easy to show that H^ is contractible . However Kuiper has used the queer 7 6 differential structures on S to show that either TT° (H„) 0 5 or 0 .

0 Corollary 2 . If X C K , and N , N^ are regular neighbourhoods of X in M , such that N ^ : N , then N - N^ = N x I . Proof . Construct two derived neighbourhoods as in the proof of Lemma 14 . N* = f"^ [ 0 ,6 J , N* ^ f"^ [O , S where 0 < 6< 1 . 1 Then / - N* = f"^ [ S , = f'^ t X I = ii* x I . Therefore the result is true for N* , N* . By Theorem 8 (2) choose a - 25 - homeomorphism h ! N*—^, N keeping X fixed . Now h N* , N 0 1 J- are both regular neighbourhoods of X in N , and so by Theorem 8 (3) we can ambient isotope h N* onto N^ keeping N fixed .

Let X be the space obtained by identifying the intervals x y = xy' , xz of y z in X . xz' , and let Y be the image - 26 - X Then X 0 conewise , axid Y 0 because Y is an arc . But X Y because any initial elementary simplicial collapse of any triangulation of X must have its free face in Y , and so must remove part of B . Similarly can build examples to show that X Y ^ /v XuY 0 XnYRemark 2 . Corollary 4 is useful for simplifying ^ines . For example the spine of a bounded 3-manifold can be normalised in the following sense : we can find a spine , which is a 2-dimensional cell complex in which every edge bounds exactly 3 faces , and every vertex bounds exactly 4 edges and 6 faces .

Download PDF sample

Rated 4.72 of 5 – based on 47 votes