Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Normal view MARC view ISBD view

The Geometric Hopf Invariant and Surgery Theory [electronic resource] / by Michael Crabb, Andrew Ranicki.

By: Crabb, Michael [author.].
Contributor(s): Ranicki, Andrew [author.] | SpringerLink (Online service).
Material type: TextTextSeries: Springer Monographs in Mathematics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Description: XVI, 397 p. 1 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319713069.Subject(s): Algebraic topology | Cell aggregation -- Mathematics | Algebraic Topology | Manifolds and Cell Complexes (incl. Diff.Topology)Additional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 514.2 Online resources: Click here to access online
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 -- A The homotopy Umkehr map -- B Notes on Z2-bordism -- C The geometric Hopf invariant and double points (2010) -- References -- Index.
In: Springer eBooksSummary: 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. .
Tags from this library: No tags from this library for this title. Log in to add tags.
No physical items for this record

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.

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. .

There are no comments for this item.

Log in to your account to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in


Visitor Counter