The Geometric Hopf Invariant and Surgery Theory
Michael Crabb, Andrew Ranicki
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Springer International Publishing
Naturwissenschaften, Medizin, Informatik, Technik / Geometrie
Beschreibung
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.Kundenbewertungen
difference construction chain homotopy, MSC (2010): 55Q25, 57R42, difference construction homotopy, manifolds, double point theorem, doube points of maps, Z_2 equivariant homotopy, algebraic surgery, surgery obstruction theory, inner product spaces, bordism theory, stable homotopy theory, geometric Hopf invariant, coordinate-free approach to stable homotopy theory