Lectures on Homotopy Theory (PDF)

Name: Lectures on Homotopy Theory
Brand: Elsevier Science & Techn.
SKU: 31196935
Price: 54.95 EUR
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(Sprache: Englisch)

Autor: R. A. Piccinini

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Lectures on Homotopy Theory, R. A. Piccinini

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The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is...

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The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the n^th homotopy group of the sphere Sⁿ, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sⁿ are trivial and that the third homotopy group of S² is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps.

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.

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Bibliographische Angaben

Autor: R. A. Piccinini
1992, 292 Seiten, Englisch
Verlag: Elsevier Science & Techn.
ISBN-10: 0080872824
ISBN-13: 9780080872827
Erscheinungsdatum: 21.01.1992

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Peter J. Eccles
Throughout the book results are proved in detail and with great care and the exercises reinforce the techniques developed... the author has certainly achieved the objective which he sets out in his preface.
Mathematical Reviews
...a good introduction to the homotopy theory of topological spaces suitable for beginning graduate students... can be recommended...
European Mathematical Society Newsletter

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