The Geometric Hopf Invariant and Surgery Theory

Michael Crabb, Andrew Ranicki

$278.95 $222.98

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English

Springer International Publishing AG
06 June 2019

Topology; Algebraic topology

Series: 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.

By: Michael Crabb, Andrew Ranicki
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2017
Dimensions: Height: 235mm, Width: 155mm,
Weight: 635g
ISBN: 9783319890616
ISBN 10: 3319890611
Series: Springer Monographs in Mathematics
Pages: 397
Publication Date: 06 June 2019
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Paperback
Publisher's Status: Active

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.

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The Geometric Hopf Invariant and Surgery Theory

Michael Crabb, Andrew Ranicki

$278.95 $222.98

Paperback

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