The Geometric Hopf Invariant and Surgery Theory

Softcover Nachdruck of the original 1. Auflage 2017
ISBN: 978-3-319-89061-6
Verlag: Springer International Publishing

Buch, Englisch, 397 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 628 g

Reihe: Springer Monographs in Mathematics

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds.

Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists.
Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, withmany results old and new.

Zielgruppe

Research

Autoren/Hrsg.

Ranicki, Andrew

Crabb, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

1 The difference construction.- 2 Umkehr maps and inner product spaces.- 3 Stable homotopy theory.- 4 Z_2-equivariant homotopy and bordism theory.- 5 The geometric Hopf invariant.- 6 The double point theorem.- 7 The -equivariant geometric Hopf invariant.- 8 Surgery obstruction theory.- A The homotopy Umkehr map.- B Notes on Z2-bordism.- C The geometric Hopf invariant and double points (2010).- References.- Index.