Read e-book online A Course in Simple-Homotopy Theory PDF

By M.M. Cohen

ISBN-10: 0387900551

ISBN-13: 9780387900551

ISBN-10: 038790056X

ISBN-13: 9780387900568

ISBN-10: 3540900551

ISBN-13: 9783540900559

This booklet grew out of classes which I taught at Cornell college and the collage of Warwick in the course of 1969 and 1970. I wrote it due to a robust trust that there will be on hand a semi-historical and geo­ metrically prompted exposition of J. H. C. Whitehead's appealing concept of simple-homotopy forms; that tips on how to comprehend this concept is to grasp how and why it used to be equipped. This trust is buttressed through the truth that the most important makes use of of, and advances in, the idea in contemporary times-for instance, the s-cobordism theorem (discussed in §25), using the speculation in surgical procedure, its extension to non-compact complexes (discussed on the finish of §6) and the evidence of topological invariance (given within the Appendix)-have come from simply such an knowing. A moment cause of writing the ebook is pedagogical. this can be an outstanding topic for a topology pupil to "grow up" on. The interaction among geometry and algebra in topology, each one enriching the opposite, is fantastically illustrated in simple-homotopy idea. the topic is offered (as within the classes pointed out on the outset) to scholars who've had an excellent one­ semester direction in algebraic topology. i've got attempted to jot down proofs which meet the desires of such scholars. (When an explanation used to be passed over and left as an workout, it used to be performed with the welfare of the coed in brain. He should still do such routines zealously.

Show description

Read Online or Download A Course in Simple-Homotopy Theory PDF

Similar topology books

Download e-book for kindle: Point set topology by Paul A. Smith, Samuel Eilenberg

Appropriate for an entire path in topology, this article additionally services as a self-contained therapy for self sufficient examine. extra enrichment fabrics and complex subject coverage—including large fabric on differentiable manifolds, summary harmonic research, and stuck element theorems—constitute an outstanding reference for arithmetic lecturers, scholars, and execs.

Download e-book for kindle: Lectures on Chaotic Dynamical Systems by V. S. Afraimovich, Sze-Bi Hsu

This ebook is dedicated to chaotic nonlinear dynamics. It offers a constant, updated creation to the sphere of wierd attractors, hyperbolic repellers, and nonlocal bifurcations. The authors preserve the top attainable point of 'physical' instinct whereas staying mathematically rigorous. furthermore, they clarify numerous very important nonstandard algorithms and difficulties related to the computation of chaotic dynamics.

New PDF release: Topology: An Introduction to the Point-Set and Algebraic

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

Extra resources for A Course in Simple-Homotopy Theory

Sample text

Thus v,j ! a1' is null homotopic in L and, L being arc-wise connected , it is homotopic to the constant map at eO. Therefore by (7. 1 ) , L u Uej A L u U ej, rei L where the ej are trivially attached at eO. 9) L u U ej u U er + 1 A L u Uej u UfT + 1 • Now let the f:+ 1 have characteristic maps

If (K, L) and (K', L) are homotopically trivial CW pairs, define (K, L) '" (K', L) iff K A K' reI L. This is clearly an equivalence relation and we let [K, L] denote the equivalence class of (K, L). An addition of equivalence classes is defined by setting [K,. of K and K' identified by the identity map L on L. 2 it doesn't matter which "disjoint union of K and K' identified . . " we take. 2) the equivalence classes form a set, since the isomorphism classes of finite CW complexes can easily be seen to have cardinality :s; 2c.

1) Suppose that (P, Po) is a C W pair with P = I a Po u U e'/, where Po is ;=1 connected. Suppose that 'P i : (/"' I" - I , r - I ) � (P, Po ; eO ) are characteristic maps for the e7 and that either: a) n ;::: 3, or b) n = 2 and 'P i(O/") = eO for all i. (P, Po ; eO ) is a free l1T l -module with basis ['Pd, ['P2 ], . . , ['Pa]' PROOF: We claim first that the inclusion map induces an isomorphism i# : 1Tl(PO , eO ) � 1Tl (P, eO), For all n ;::: 2, i# is onto because, by the cellular approximation theorem , any map of (/ 1 , al l ) into (P, eO) can be homotoped rel al l into Po.

Download PDF sample

A Course in Simple-Homotopy Theory by M.M. Cohen


by James
4.1

Rated 4.73 of 5 – based on 25 votes

admin