Download e-book for iPad: A Course in Simple-Homotopy Theory by M.M. Cohen

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 collage and the collage of Warwick in the course of 1969 and 1970. I wrote it as a result of a robust trust that there might be available a semi-historical and geo­ metrically encouraged exposition of J. H. C. Whitehead's attractive thought of simple-homotopy kinds; that tips on how to comprehend this idea is to understand how and why it was once outfitted. This trust is buttressed by means of the truth that the foremost makes use of of, and advances in, the speculation in fresh times-for instance, the s-cobordism theorem (discussed in §25), using the idea in surgical procedure, its extension to non-compact complexes (discussed on the finish of §6) and the facts of topological invariance (given within the Appendix)-have come from simply such an realizing. A moment explanation for writing the booklet is pedagogical. this is often a great topic for a topology scholar to "grow up" on. The interaction among geometry and algebra in topology, each one enriching the opposite, is fantastically illustrated in simple-homotopy conception. the topic is available (as within the classes pointed out on the outset) to scholars who've had a very good one­ semester direction in algebraic topology. i've got attempted to put in writing proofs which meet the desires of such scholars. (When an evidence used to be passed over and left as an workout, it used to be performed with the welfare of the scholar in brain. He may still do such routines zealously.

Show description

Read or Download A Course in Simple-Homotopy Theory PDF

Similar topology books

Read e-book online Surveys on surgery theory PDF

Surgical procedure concept, the foundation for the category conception of manifolds, is now approximately 40 years outdated. there were a few impressive accomplishments in that point, that have resulted in greatly various interactions with algebra, research, and geometry. staff in lots of of those components have frequently lamented the shortcoming of a unmarried resource that surveys surgical procedure thought and its purposes.

Michael F. Barnsley, Mathematics's Fractals Everywhere PDF

This quantity is the revised moment variation of the unique publication, released in 1988. It contains extra difficulties and instruments emphasizing fractal functions, in addition to an all-new resolution key to the textual content workouts. The revision contains new chapters on vector recurrent iterated functionality structures and alertness of fractals.

Download e-book for kindle: Introduction to symplectic topology by Dusa McDuff, Dietmar Salamon

This primary variation of this publication fast turned a longtime textual content during this fast-developing department of arithmetic. This moment variation has been considerably revised and increased. It incorporates a part on new advancements and an extended dialogue of Taubes' and Donaldson's contemporary effects.

Additional resources for A Course in Simple-Homotopy Theory

Sample text

Then the 1 x 1 matrix ( l - ab) is not an eiementary matrix, but since it represents the same element in Wh(G) as 0 -1 1 a -1 1 0 1 a I ab 0 2 (- ) ( )( )( ) ( ) 0 its torsion is O. ' = b i O I ' b I O I ' Algebra 42 §11. Some information about Whitehead groups In the last section we defined, for any group G, the abelian group Wh(G) given by Wh(G) = KTCIG) where T is the group of trivial units of lLG. The com putation of WHITEHEAD groups is a difficult and interesting task for which there has developed, in recent years, a rich literature.

L x [ - I , O] = [L, L] = since L x [ - I , I ] '\( L == L x I . 0 In pictures, these equations represent \ This completes the proof. 9), determines the deformation (M, u K) A (M, u K) up L 2 L, L, = K Ll L2 , reI L 2 . J It follows directly from the second definition that f* is a group homo­ morphism. 6) it follows directly that g* f* = (gf) * . 2) There is a covariant functor from the category offinite CW complexes and cellular maps to the category of abelian groups and group homomorphisms given by L ......

We call this last complex M. 7), these 'numbers are precisely equal to the ranks of the free (integral) homology modules H (M r U L, L) r and H (M, M r U L). (M, L) 1 ranks are equal. 0 = O. Thus d is an isomorphism and these §S. Matrices and formal deformations Given a homotopically trivial CW pair, we have shown that it can be transformed into a pair in simplified form. So consider a simplified pair (K, L) ; K = L u Uej u Uer + 1 where the ej are trivially attached at eO . W + 1 : 81' + 1 --+ L u U ej, where 'Pi is a characteristic map for er+ 1 .

Download PDF sample

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

by John

Rated 4.13 of 5 – based on 3 votes