Hopf Spaces (eBook)

eBook Download: PDF

1976 | 1. Auflage
222 Seiten
Elsevier Science (Verlag)
978-0-08-087133-2 (ISBN)

Infos

Hopf spaces

Inhalt

Front Cover 1
Hopf Spaces 4
Copyright Page 5
Table of Contents 6
Introduction 10
Chapter 0. Notations, conventions and preliminary observations 12
0.1 Spaces and maps 12
0.2 Homotopies 12
0.3 Categories and adjoint maps 13
0.4 Pullbacks, pushouts and Eckmann-Hilton duality 14
0.5 O–spectra, ring spectra, generalized cohomology 15
Chapter I. The category of H–spaces 19
Introduction 19
1.1 Basic properties of H–spaces 20
1.2 Some special classes of H–spaces 30
1.3 The structure of [ , H–space] 32
1.4 H–deviation and H–homotopy equivalence 36
1.5 Change of H–structures and H–maps 40
Chapter II. Homotopy properties of H–spaces 45
Introduction 45
2.1 H–spaces and fibrations 45
2.2 H–liftings 48
2.3 Postnikov systems 53
2.4 Actions, H–actions and principal fibrations 58
2.5 HA and HC obstructions 69
2.6 Homotopy solvability and homotopy nilpotency 74
Chapter III. The cohomology of H–spaces 80
Introduction 80
3.1 The Hopf algebra H*(X,Zp ) 81
3.2 Some relations between the algebra H*(X,Zp) and the coalgebra H*( OX, Zp ) 84
3.3 Browder's Bockstein spectral sequence 95
3.4 High order operations 109
Chapter IV. Mod p theory of H–spaces 124
Introduction 124
4.1 p–equivalence and p–universal spaces 125
4.2 mod p–homotopy 135
4.3 Decomposition of o–equivalences 139
4.4 A study of Ho spaces 145
4.5 Mod P1 H–spaces 147
4.6 The genus of an H–space 158
4.7 Mixing homotopy types 163
4.8 The non classical H–spaces and other applications 168
Chapter V. Non stable BP resolutions 174
Introduction 174
5.1 Killing homology p–torsion 175
5.2 Wilson's B(n,p)'s 183
5.3 The groups [ , B(n,p)] 187
5.4 H–maps into B(n,p) 192
5.5 Examples: Some properties of BU 198
5.6 Non stable BP Adams resolutions 201
5.7 Some simple applications 209
Bibliography 222
List of symbols 230
Index of terminology 233

Produkt-Details

• Erscheint lt. Verlag: 1.1.1976
• Mitarbeit: Herausgeber (Serie): Alexander Zabrodsky
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-087133-X / 008087133X
• ISBN-13: 978-0-08-087133-2 / 9780080871332