The geometric Hopf invariant and surgery theory / by Michael Crabb, Andrew Ranicki.

Format:

Book

Author/Creator:

Crabb, M. C. (Michael Charles), author.

Ranicki, Andrew, 1948- author.

Series:

Springer monographs in mathematics 1439-7382

Springer Monographs in Mathematics, 1439-7382

Language:

English

Subjects (All):

Algebraic topology.

Homotopy theory.

Manifolds (Mathematics).

Complex manifolds.

Invariants.

Physical Description:

xvi, 397 pages : illustrations (1 in color) ; 25 cm.

Place of Publication:

Cham : Springer International Publishing, [2018]

Contents:

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

Appendix A: The homotopy Umkehr map

Appendix B: Notes on Z2-bordism

Appendix C: The geometric Hopf invariant and double points (2010)

References

Index.

Notes:

"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." - publisher

Includes bibliographical references and index.

ISBN:

3319713051

9783319713052

OCLC:

1007045576