The Resource A Guide to the Classification Theorem for Compact Surfaces, by Jean Gallier, Dianna Xu, (electronic resource)

A Guide to the Classification Theorem for Compact Surfaces, by Jean Gallier, Dianna Xu, (electronic resource)

Label
A Guide to the Classification Theorem for Compact Surfaces
Title
A Guide to the Classification Theorem for Compact Surfaces
Statement of responsibility
by Jean Gallier, Dianna Xu
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology
Member of
http://library.link/vocab/creatorName
Gallier, Jean
Image bit depth
0
LC call number
QA611-614.97
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Xu, Dianna.
  • SpringerLink
Series statement
Geometry and Computing,
Series volume
9
http://library.link/vocab/subjectName
  • Mathematics
  • Topology
  • Algebraic topology
  • Cell aggregation
  • Mathematics
  • Topology
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Algebraic Topology
Label
A Guide to the Classification Theorem for Compact Surfaces, by Jean Gallier, Dianna Xu, (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
The Classification Theorem: Informal Presentation -- Surfaces -- Simplices, Complexes, and Triangulations -- The Fundamental Group, Orientability -- Homology Groups -- The Classification Theorem for Compact Surfaces -- Viewing the Real Projective Plane in R3 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes
Dimensions
unknown
Extent
XII, 178 p. 40 illus., 20 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783642343643
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-642-34364-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-642-34364-3
Label
A Guide to the Classification Theorem for Compact Surfaces, by Jean Gallier, Dianna Xu, (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
The Classification Theorem: Informal Presentation -- Surfaces -- Simplices, Complexes, and Triangulations -- The Fundamental Group, Orientability -- Homology Groups -- The Classification Theorem for Compact Surfaces -- Viewing the Real Projective Plane in R3 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes
Dimensions
unknown
Extent
XII, 178 p. 40 illus., 20 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783642343643
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-642-34364-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-642-34364-3

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