Algebraic Topology: An Intuitive Approach by Hajime Sato PDF

By Hajime Sato

ISBN-10: 0821810464

ISBN-13: 9780821810460

The only so much tough factor one faces while one starts to profit a brand new department of arithmetic is to get a suppose for the mathematical experience of the topic. the aim of this booklet is to assist the aspiring reader collect this crucial good judgment approximately algebraic topology in a quick time period. To this finish, Sato leads the reader via uncomplicated yet significant examples in concrete phrases. in addition, effects will not be mentioned of their maximum attainable generality, yet by way of the easiest and so much crucial situations.

In reaction to feedback from readers of the unique variation of this publication, Sato has additional an appendix of precious definitions and effects on units, basic topology, teams and such. He has additionally supplied references.

Topics coated comprise primary notions akin to homeomorphisms, homotopy equivalence, basic teams and better homotopy teams, homology and cohomology, fiber bundles, spectral sequences and attribute periods. items and examples thought of within the textual content comprise the torus, the Möbius strip, the Klein bottle, closed surfaces, mobile complexes and vector bundles.

Show description

Read or Download Algebraic Topology: An Intuitive Approach PDF

Similar topology books

An Introduction to Topology & Homotopy - download pdf or read online

The therapy of the topic of this article isn't encyclopedic, nor was once it designed to be appropriate as a reference guide for specialists. really, it introduces the themes slowly of their historical demeanour, in order that scholars aren't crushed by means of the final word achievements of numerous generations of mathematicians.

Geometric Theory of Functions of a Complex Variable - download pdf or read online

This ebook is predicated on lectures on geometric functionality conception given via the writer at Leningrad kingdom collage. It reports univalent conformal mapping of easily and multiply hooked up domain names, conformal mapping of multiply hooked up domain names onto a disk, purposes of conformal mapping to the research of inside and boundary houses of analytic capabilities, and normal questions of a geometrical nature facing analytic capabilities.

Read e-book online The Lefschetz Centennial Conference, Part 2: Proceedings on PDF

Includes a number of the papers within the quarter of algebraic topology awarded on the 1984 Solomon Lefschetz Centennial convention held in Mexico urban

Additional info for Algebraic Topology: An Intuitive Approach

Example text

Am 1 + b m 1 am 2 + b m 2 . . define their sum a1 n + b1 n a2 n + b2 n .. am n + bm n    .  For any matrix A = (ai j ), we let −A be the matrix (−ai j ). Given a scalar λ ∈ K, we define the matrix λA as the matrix C = (ci j ) such that ci j = λai j ; that is     a1 1 a1 2 . . a1 n λa1 1 λa1 2 . . λa1 n  a2 1 a2 2 . . a2 n   λa2 1 λa2 2 . . λa2 n      λ  .. ..  =  .. ..  . . .  . . .   . .  am 1 am 2 . . am n λam 1 λam 2 . . 1. MATRICES Given an m × n matrices A = (ai k ) and an n × p matrices B = (bk j ), we define their product AB as the m × p matrix C = (ci j ) such that n ci j = ai k b k j , k=1 for 1 ≤ i ≤ m, and 1 ≤ j ≤ p.

A1n  a21 a22 . . a2n     .. ..  .  . .  am1 am2 . . amn and v1 v2 .. vn g(u1 ) g(u2 )  b11 b12  b21 b22   ..  . bn1 bn2 . . g(up )  . . b1p . . b2p   ..  .. .  . . 1. MATRICES for all k, 1 ≤ k ≤ n, and for every y = y1 v1 + · · · + yn vn , letting f (y) = z = z1 w1 + · · · + zm wm , we have n zi = ai k y k (3) k=1 for all i, 1 ≤ i ≤ m. Then, if y = g(x) and z = f (y), we have z = f (g(x)), and in view of (2) and (3), we have p n zi = bk j x j ) ai k ( j=1 k=1 n p = ai k b k j x j k=1 j=1 p n = ai k b k j x j j=1 k=1 p n = ai k bk j )xj .

8 implies that |I| ≤ |J|. A symmetric argument yields |J| ≤ |I|. 9 also holds for vector spaces that are not finitely generated. When E is not finitely generated we say that E is of infinite dimension. The dimension of a finitely generated vector space E is the common dimension n of all of its bases and is denoted by dim(E). Clearly, if the field R itself is viewed as a vector space, then every family (a) where a ∈ R and a = 0 is a basis. Thus dim(R) = 1. Note that dim({0}) = 0. If E is a vector space of dimension n ≥ 1, for any subspace U of E, if dim(U ) = 1, then U is called a line; if dim(U ) = 2, then U is called a plane; if dim(U ) = n − 1, then U is called a hyperplane.

Download PDF sample

Algebraic Topology: An Intuitive Approach by Hajime Sato


by Anthony
4.3

Rated 4.97 of 5 – based on 13 votes