Stable Homotopy Around the Arf-Kervaire Invariant (eBook)

Victor P. Snaith (Autor)

eBook Download: PDF

2009 | 2009
XIV, 239 Seiten
Springer Basel (Verlag)
978-3-7643-9904-7 (ISBN)

Infos

Were I to take an iron gun, And ?re it o? towards the sun; I grant 'twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, 'Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .

Inhalt

Contents 6
Preface 8
Algebraic Topology Background 16
The Arf-Kervaire Invariant via QX 48
The Upper Triangular Technology 63
A Brief Glimpse of Algebraic K-theory 79
The Matrix Corresponding to 106
Real Projective Space 132
Hurewicz Images, BP-theory and the Arf-Kervaire Invariant 156
Upper Triangular Technology and the Arf-Kervaire Invariant 167
Futuristic and Contemporary Stable Homotopy 210
Bibliography 227
Index 244

Produkt-Details

• Erscheint lt. Verlag: 28.3.2009
• Reihe/Serie: Progress in Mathematics
• Reihe/Serie: Progress in Mathematics
• Zusatzinfo: XIV, 239 p.
• Verlagsort: Basel
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• Schlagworte: Adams operation • Algebraic K-Theory • algebraic topology • Arf-Kervaire invariant • Homotopy • homotopy theory • K-theory • manifold • stable homotopy • upper triangular technology
• ISBN-10: 3-7643-9904-X / 376439904X
• ISBN-13: 978-3-7643-9904-7 / 9783764399047