The Resource Mod Two Homology and Cohomology, by Jean-Claude Hausmann, (electronic resource)

Mod Two Homology and Cohomology, by Jean-Claude Hausmann, (electronic resource)

Label
Mod Two Homology and Cohomology
Title
Mod Two Homology and Cohomology
Statement of responsibility
by Jean-Claude Hausmann
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: It leads more quickly to the essentials of the subject, An absence of signs and orientation considerations simplifies the theory, Computations and advanced applications can be presented at an earlier stage, Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book
Member of
http://library.link/vocab/creatorName
Hausmann, Jean-Claude
Dewey number
514.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
2Hn--XqwPuU
Image bit depth
0
Language note
English
LC call number
QA612-612.8
Literary form
non fiction
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Algebraic topology
  • Cell aggregation
  • Algebraic Topology
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
Mod Two Homology and Cohomology, by Jean-Claude Hausmann, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
Introduction -- Simplicial (co)homology -- Singular and cellular (co)homologies -- Products -- Poincar ́e Duality -- Projective spaces -- Equivariant cohomology -- Steenrod squares -- Stiefel-Whitney classes -- Miscellaneous applications and developments -- Hints and answers for some exercises
Dimensions
unknown
Edition
1st ed. 2014.
Extent
1 online resource (IX, 535 p. 9 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783319093543
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-319-09354-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3710000000343722
  • (SSID)ssj0001424537
  • (PQKBManifestationID)11849599
  • (PQKBTitleCode)TC0001424537
  • (PQKBWorkID)11369462
  • (PQKB)10245699
  • (DE-He213)978-3-319-09354-3
  • (EXLCZ)993710000000343722
Label
Mod Two Homology and Cohomology, by Jean-Claude Hausmann, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
Introduction -- Simplicial (co)homology -- Singular and cellular (co)homologies -- Products -- Poincar ́e Duality -- Projective spaces -- Equivariant cohomology -- Steenrod squares -- Stiefel-Whitney classes -- Miscellaneous applications and developments -- Hints and answers for some exercises
Dimensions
unknown
Edition
1st ed. 2014.
Extent
1 online resource (IX, 535 p. 9 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783319093543
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-319-09354-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3710000000343722
  • (SSID)ssj0001424537
  • (PQKBManifestationID)11849599
  • (PQKBTitleCode)TC0001424537
  • (PQKBWorkID)11369462
  • (PQKB)10245699
  • (DE-He213)978-3-319-09354-3
  • (EXLCZ)993710000000343722

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