Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has been occupying an increasingly prominent place in the field of algebraic topology.
An edition of An Introduction to Homotopy Theory
(1953)
An introduction to homotopy theory
by Peter Hilton
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Homotopy theory, TopologyShowing 3 featured editions. View all 3 editions?
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Book Details
First Sentence
"Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has been occupying an increasingly prominent place in the field of algebraic topology."
Table of Contents
I. INTRODUCTION
II. THE HOMOTOPY GROUPS
1. Definition of the absolute homotopy groups
2. Alternative descriptions of the homotopy groups
3. The role of the base-point; operation of $pi_1(Y,y_0)$ on $pi_n(Y,y_0)$
4. The relative homotopy groups
III. THE CLASSICAL THEOREMS OF HOMOTOPY THEORY
1. The simplicial approximation theorem
2. The Brouwer degree
3. The Hurewicz isomorphism theorem
IV. THE EXACT HOMOTOPY SEQUENCE
1. Definition of the sequence
2. Proof of exactness
3. Properties of the homotopy sequence
4. The group $pi_2(Y, Y0)$
5. Special cases
6. The homotopy groups of the union of two spaces
7. The homotopy sequence of a triple
V. FIBRE-SPACES
1. Definitions and fundamental theorems
2. The Hopf fibrings
3. Fibre-spaces over spheres
4. Appendix on pseudo-fibre-spaces
VI. THE HOPF INVARIANT AND SUSPENSION THEOREMS
1. The Hopf invariant
2. The Freudenthal suspension and its generalization
3. Application to fibre-spaces
4. The generalized Hopf invariant
VII. WHITEHEAD CELL-COMPLEXES
1. Definition of a cell-complex, and the basic properties of CW-complexes
2. The n-type of a complex and the Massey homology spectrum
3. Realizability theorems
VIII. HOMOTOPY GROUPS OF COMPLEXES
1. Statement of the problem
2. Whitehead's exact-sequence
3. The homology system and the reduced complex
4. Normal complex of S. C. Chang
5. Appendix
Bibliography
Index and Glossary
Edition Notes
First printed 1953
Reprinted 1961,1964,1966
ID Numbers
Excerpts
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History
- Created September 15, 2008
- 17 revisions
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| November 14, 2021 | Edited by dcapillae | Merge works |
| December 15, 2009 | Edited by WorkBot | link works |
| May 16, 2009 | Edited by netrapture | adding more to TOC |
| May 16, 2009 | Edited by netrapture | adding more to TOC |
| September 15, 2008 | Created by ImportBot | Imported from University of Toronto MARC record |