The Geometric Hopf Invariant and Surgery Theory, Softcover reprint of the original 1st ed. 2017 Springer Monographs in Mathematics Series
Auteurs : Crabb Michael, Ranicki Andrew
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, with many results old and new.Provides the homotopy theoretic foundations for surgery theory
Includes a self-contained account of the Hopf invariant in terms of Z_2-equivariant homotopy
Covers applications of the Hopf invariant to surgery theory, in particular the Double Point Theorem
Date de parution : 06-2019
Ouvrage de 397 p.
15.5x23.5 cm
Date de parution : 02-2018
Ouvrage de 397 p.
15.5x23.5 cm
Mots-clés :
MSC (2010): 55Q25, 57R42, geometric Hopf invariant, manifolds, doube points of maps, double point theorem, algebraic surgery, difference construction homotopy, difference construction chain homotopy, coordinate-free approach to stable homotopy theory, inner product spaces, stable homotopy theory, Z_2 equivariant homotopy, bordism theory, surgery obstruction theory
