Stable Homotopy Around the Arf-Kervaire In...

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Beschreibung

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 .

Zusammenfassung

Introduction of the new "upper triangular technology" method

Detailed application of upper triangular technology to operations in algebraic K-theory and to the Arf-Kervaire invariant problem.

An account of the relation of the book's classical stable homotopy theory results to the important, new motivic stable homotopy theory of Morel-Voevodsky

Includes supplementary material: [...]

Inhaltsverzeichnis

Algebraic Topology Background.- The Arf-Kervaire Invariant via QX.- The Upper Triangular Technology.- A Brief Glimpse of Algebraic K-theory.- The Matrix Corresponding to 1 ? ?3.- Real Projective Space.- Hurewicz Images, BP-theory and the Arf-Kervaire Invariant.- Upper Triangular Technology and the Arf-Kervaire Invariant.- Futuristic and Contemporary Stable Homotopy.

Details

Erscheinungsjahr:	2009
Fachbereich:	Topologie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Progress in Mathematics
Inhalt:	xiv 239 S.
ISBN-13:	9783764399030
ISBN-10:	3764399031
Sprache:	Englisch
Herstellernummer:	12263998
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Snaith, Victor P.
Hersteller:	Springer Basel Birkhäuser Basel Springer Basel AG Progress in Mathematics
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 20 mm
Von/Mit:	Victor P. Snaith
Erscheinungsdatum:	19.02.2009
Gewicht:	0,559 kg

Artikel-ID: 101694212