Lectures on Homotopy Theory - 1st Edition - ISBN: 9780444892386, 9780080872827

Lectures on Homotopy Theory, Volume 171

1st Edition

Authors: R.A. Piccinini
Hardcover ISBN: 9780444892386
eBook ISBN: 9780080872827
Imprint: North Holland
Published Date: 21st January 1992
Page Count: 292
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Table of Contents

  1. Homotopy Groups. 1.1 Function Spaces. 1.2 H-Spaces and CoH-Spaces. 1.3 Homotopy Groups. 2. Fibrations and Cofibrations. 2.1 Pullbacks and Pushouts. 2.2 Fibrations. 2.3 Cofibrations. 2.4 Applications of the Mapping Cylinder. 3. Exact Homotopy Sequences. 3.1 Exact Sequence of a Map: Covariant Case. 3.2 Exact Sequence of a Map: Contravariant Case. 4. Simplicial Complexes. 4.1 Simplicial Complexes. 4.2 Simplicial Approximation Theorem. 4.3 Polyhedra. 4.4 Fibrations and Polyhedra. 5. Relative Homotopy Groups. 5.1 Homotopy Groups of Maps. 5.2 Quasifibrations. 5.3 Some Homotopy Groups of spheres. 6. Homotopy Theory of CW-complexes. 6.1 CW-complexes. 6.2 Homotopy theory of CW-complexes. 6.3 Eilenberg-Mac Lane spaces. 7. Fibrations revisited. 7.1 Sections of fibrations. 7.2 F-fibrations. 7.3 Universal F-fibrations. Appendix: Colimits. Compactly generated spaces. Index.

Description

  1. Homotopy Groups. 1.1 Function Spaces. 1.2 H-Spaces and CoH-Spaces. 1.3 Homotopy Groups. 2. Fibrations and Cofibrations. 2.1 Pullbacks and Pushouts. 2.2 Fibrations. 2.3 Cofibrations. 2.4 Applications of the Mapping Cylinder. 3. Exact Homotopy Sequences. 3.1 Exact Sequence of a Map: Covariant Case. 3.2 Exact Sequence of a Map: Contravariant Case. 4. Simplicial Complexes. 4.1 Simplicial Complexes. 4.2 Simplicial Approximation Theorem. 4.3 Polyhedra. 4.4 Fibrations and Polyhedra. 5. Relative Homotopy Groups. 5.1 Homotopy Groups of Maps. 5.2 Quasifibrations. 5.3 Some Homotopy Groups of spheres. 6. Homotopy Theory of CW-complexes. 6.1 CW-complexes. 6.2 Homotopy theory of CW-complexes. 6.3 Eilenberg-Mac Lane spaces. 7. Fibrations revisited. 7.1 Sections of fibrations. 7.2 F-fibrations. 7.3 Universal F-fibrations. Appendix: Colimits. Compactly generated spaces. Index.

Details

No. of pages:
292
Language:
English
Copyright:
© North Holland 1992
Published:
Imprint:
North Holland
eBook ISBN:
9780080872827

Reviews

@from:Peter J. Eccles @qu: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. @source:Mathematical Reviews @qu:...a good introduction to the homotopy theory of topological spaces suitable for beginning graduate students... can be recommended... @source:European Mathematical Society Newsletter


About the Authors

R.A. Piccinini Author

Affiliations and Expertise

University of Milan, Italy