The Geometric Hopf Invariant and Surgery Theory

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book The Geometric Hopf Invariant and Surgery Theory by Michael Crabb, Andrew Ranicki, Springer International Publishing
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Author: Michael Crabb, Andrew Ranicki ISBN: 9783319713069
Publisher: Springer International Publishing Publication: January 24, 2018
Imprint: Springer Language: English
Author: Michael Crabb, Andrew Ranicki
ISBN: 9783319713069
Publisher: Springer International Publishing
Publication: January 24, 2018
Imprint: Springer
Language: English

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. 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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. 

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