Lectures on Homotopy Theory
Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.
307 pages; ISBN 9780080872827
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Title: Lectures on Homotopy Theory
Author: R.A. Piccinini
IB Mathematics Higher Level 2012 US$ 67.20 832 pages
IB Mathematical Studies Standard 2012 US$ 53.60 624 pages