An introduction to homotopy theory
By: Peter J. Hilton.
Series: Cambridge tracts in mathematics and mathematical physics -- no. 43
Publisher: University Press
Published: 1961
Place of publication: Cambridge
Language: eng
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.
Notes: First printed 1953
Reprinted 1961,1964,1966
Table of contents: label: I
title: INTRODUCTION
pagenum: vii; label: II
title: THE HOMOTOPY GROUPS; label: 1
title: Definition of the absolute homotopy groups
pagenum: 5; label: 2
title: Alternative descriptions of the homotopy groups
pagenum: 8; label: 3
title: The role of the base-point; operation of $pi_1(Y,y_0)$ on $pi_n(Y,y_0)$
pagenum: 11; label: 4
title: The relative homotopy groups
pagenum: 16; label: III
title: THE CLASSICAL THEOREMS OF HOMOTOPY THEORY; label: 1
title: The simplicial approximation theorem
pagenum: 24; label: 2
title: The Brouwer degree
pagenum: 25; label: 3
title: The Hurewicz isomorphism theorem
pagenum: 30; label: IV
title: THE EXACT HOMOTOPY SEQUENCE; label: 1
title: Definition of the sequence
pagenum: 34; label: 2
title: Proof of exactness
pagenum: 35; label: 3
title: Properties of the homotopy sequence
pagenum: 37; label: 4
title: The group $pi_2(Y, Y0)$
pagenum: 39; label: 5
title: Special cases
pagenum: 41; label: 6
title: The homotopy groups of the union of two spaces
pagenum: 42; label: 7
title: The homotopy sequence of a triple
pagenum: 44; label: V
title: FIBRE-SPACES; label: 1
title: Definitions and fundamental theorems
pagenum: 46; label: 2
title: The Hopf fibrings
pagenum: 51; label: 3
title: Fibre-spaces over spheres
pagenum: 55; label: 4
title: Appendix on pseudo-fibre-spaces
pagenum: 63; label: VI
title: THE HOPF INVARIANT AND SUSPENSION THEOREMS; label: 1
title: The Hopf invariant
pagenum: 69; label: 2
title: The Freudenthal suspension and its generalization
pagenum: 75; label: 3
title: Application to fibre-spaces
pagenum: 84; label: 4
title: The generalized Hopf invariant
pagenum: 90; label: VII
title: WHITEHEAD CELL-COMPLEXES; label: 1
title: Definition of a cell-complex, and the basic properties of CW-complexes
pagenum: 95; label: 2
title: The n-type of a complex and the Massey homology  spectrum
pagenum: 100; label: 3
title: Realizability theorems
pagenum: 106; label: VIII
title: HOMOTOPY GROUPS OF COMPLEXES; label: 1
title: Statement of the problem
pagenum: 114; label: 2
title: Whitehead's exact-sequence
pagenum: 115; label: 3
title: The homology system and the reduced complex
pagenum: 120; label: 4
title: Normal complex of S. C. Chang
pagenum: 128; label: 5
title: Appendix
pagenum: 133; title: Bibliography
pagenum: 134; title: Index and Glossary
pagenum: 137