The Geometric Hopf Invariant and Surgery Theory (eBook)

Michael Crabb, Andrew Ranicki (Autoren)

eBook Download: PDF

2018 | 1st ed. 2017
XVI, 397 Seiten
Springer International Publishing (Verlag)
978-3-319-71306-9 (ISBN)

Infos

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. 

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 24.1.2018
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Zusatzinfo: XVI, 397 p. 1 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: algebraic surgery • bordism theory • coordinate-free approach to stable homotopy theory • difference construction chain homotopy • difference construction homotopy • doube points of maps • double point theorem • geometric Hopf invariant • Inner product spaces • Manifolds • MSC (2010): 55Q25, 57R42 • stable homotopy theory • surgery obstruction theory • Z_2 equivariant homotopy
• ISBN-10: 3-319-71306-X / 331971306X
• ISBN-13: 978-3-319-71306-9 / 9783319713069