
The Geometric Hopf Invariant and Surgery Theory
Springer (Publisher)
Published on 6. February 2018
Book
Hardback
XVI, 397 pages
978-3-319-71305-2 (ISBN)
Description
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.More details
Series
Edition
1st ed. 2017
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
1 farbige Abbildung
XVI, 397 p. 1 illus. in color.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 28 mm
Weight
787 gr
ISBN-13
978-3-319-71305-2 (9783319713052)
DOI
10.1007/978-3-319-71306-9
Schweitzer Classification
Other editions
Additional editions

Michael Crabb | Andrew Ranicki
The Geometric Hopf Invariant and Surgery Theory
Book
06/2019
Springer
€149.79
Shipment within 10-15 days

Michael Crabb | Andrew Ranicki
The Geometric Hopf Invariant and Surgery Theory
E-Book
01/2018
Springer
€139.09
Available for download
Content
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.