Joseph J. Rotman's An Introduction to Algebraic Topology (Graduate Texts in PDF

By Joseph J. Rotman

ISBN-10: 1461245761

ISBN-13: 9781461245766

Publish yr note: First released in 1988
------------------------

A transparent exposition, with routines, of the fundamental principles of algebraic topology. compatible for a two-semester path before everything graduate point, it assumes a data of element set topology and simple algebra. even if different types and functors are brought early within the textual content, over the top generality is kept away from, and the writer explains the geometric or analytic origins of summary innovations as they're brought.

Show description

Read Online or Download An Introduction to Algebraic Topology (Graduate Texts in Mathematics, Volume 119) PDF

Similar topology books

Download PDF by Paul A. Smith, Samuel Eilenberg: Point set topology

Compatible for an entire direction in topology, this article additionally capabilities as a self-contained remedy for self sustaining learn. extra enrichment fabrics and complicated subject coverage—including large fabric on differentiable manifolds, summary harmonic research, and stuck element theorems—constitute an outstanding reference for arithmetic lecturers, scholars, and pros.

Lectures on Chaotic Dynamical Systems - download pdf or read online

This ebook is dedicated to chaotic nonlinear dynamics. It offers a constant, updated advent to the sphere of odd attractors, hyperbolic repellers, and nonlocal bifurcations. The authors maintain the top attainable point of 'physical' instinct whereas staying mathematically rigorous. moreover, they clarify quite a few vital nonstandard algorithms and difficulties regarding the computation of chaotic dynamics.

Download e-book for iPad: Topology: An Introduction to the Point-Set and Algebraic by Donald W. Kahn

Very good textual content bargains accomplished insurance of easy basic topology in addition to algebraic topology, particularly 2-manifolds, overlaying areas and basic teams. The textual content is on the market to scholars on the complicated undergraduate or graduate point who're conversant with the fundamentals of actual research or complicated calculus.

Additional resources for An Introduction to Algebraic Topology (Graduate Texts in Mathematics, Volume 119)

Sample text

5. 1t o is not a very thrilling functor since its values lie in Sets, and the only thing one can do with a set is count it. Still, it is as useful as counting ordinary components (which is how one proves that S1 and I are not homeomorphic 28 1. Some Basic Topological Notions (after deleting a point)). ) of a sequence of functors. The next is 1t 1 , the fundamental group, which takes values in Groups; the others, 1t 2 , 1t 3 , ••• , are called (higher) homotopy groups and take values in Ab (we shall study these functors in Chapter 11).

8). (3) There is a category appropriate to the fundamental group functor 1t l' Define the pointed homotopy category, hTop*, as the quotient category arising The Functor 7tl 45 from the congruence of relative homotopy: if fo, fl: (X, x o) ~ (Y, Yo), then fo ~ fl rel{xo}· The objects ofhTop* are pointed spaces (X, x o), morphisms (X, x o) --+ (Y, Yo) are relative homotopy classes [f], where f: (X, x o) ~ (Y, Yo) is a pointed map, and composition is given by [h] [f] = [h 0 f] (when h, f can be composed in Top*).

If (X, xo) and (Y, Yo) are pointed spaces, then 1tl (X x Y, (xo, Yo)) ~ 1tl (X, xo) X 1tl (Y, Yo)· PROOF. Let p: (X x Y, (xo, Yo)) -+ (X, xo) and q: (X x Y, (xo, Yo)) -+ (Y, Yo) be the projections. Then (p*, q*): 1tl (X x Y, (xo, Yo)) -+ 1tl (X, xo) X 1tl (Y, Yo) is a homomorphism. In more detail, if f: I -+ X x Y is a closed path at (xo, Yo), then (p*, q*): [f] 1--+ (p* [f], q* [f]) = ([pf], [qf]). We show that (p*, q*) is an isomorphism by displaying its inverse. 5 shows that () is well defined.

Download PDF sample

An Introduction to Algebraic Topology (Graduate Texts in Mathematics, Volume 119) by Joseph J. Rotman


by James
4.5

Rated 4.82 of 5 – based on 3 votes

admin