The Resource The Geometric Hopf Invariant and Surgery Theory, by Michael Crabb, Andrew Ranicki, (electronic resource)

The Geometric Hopf Invariant and Surgery Theory, by Michael Crabb, Andrew Ranicki, (electronic resource)

Label
The Geometric Hopf Invariant and Surgery Theory
Title
The Geometric Hopf Invariant and Surgery Theory
Statement of responsibility
by Michael Crabb, Andrew Ranicki
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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.
Member of
http://library.link/vocab/creatorName
Crabb, Michael
Image bit depth
0
LC call number
QA612-612.8
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Ranicki, Andrew.
  • SpringerLink
Series statement
Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Algebraic topology
  • Manifolds (Mathematics)
  • Complex manifolds
  • Mathematics
  • Algebraic Topology
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
The Geometric Hopf Invariant and Surgery Theory, by Michael Crabb, Andrew Ranicki, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
XVI, 397 p. 1 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319713069
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-71306-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-71306-9
Label
The Geometric Hopf Invariant and Surgery Theory, by Michael Crabb, Andrew Ranicki, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
XVI, 397 p. 1 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319713069
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-71306-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-71306-9

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