The Resource Introduction to Geometry and Topology, by Werner Ballmann, (electronic resource)

Introduction to Geometry and Topology, by Werner Ballmann, (electronic resource)

Label
Introduction to Geometry and Topology
Title
Introduction to Geometry and Topology
Statement of responsibility
by Werner Ballmann
Creator
Author
Author
Subject
Language
eng
Summary
This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course
Member of
http://library.link/vocab/creatorName
Ballmann, Werner
Dewey number
514.34
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
3HnbMt1-6go
Image bit depth
0
LC call number
  • QA613-613.8
  • QA613.6-613.66
Literary form
non fiction
Series statement
Compact Textbooks in Mathematics,
http://library.link/vocab/subjectName
  • Cell aggregation
  • Global differential geometry
  • Global analysis
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Differential Geometry
  • Global Analysis and Analysis on Manifolds
Label
Introduction to Geometry and Topology, by Werner Ballmann, (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
I. First Steps in the Topology -- II. Manifolds -- III. Differential Forms and Cohomology -- IV. Geometry of Submanifolds -- A. Alternating Multilinear Forms -- B. Cochain Complexes -- Bibliography -- Index
Dimensions
unknown
Edition
1st ed. 2018.
Extent
1 online resource (X, 169 p. 28 illus., 20 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783034809832
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-0348-0983-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4100000005323336
  • (DE-He213)978-3-0348-0983-2
  • (EXLCZ)994100000005323336
Label
Introduction to Geometry and Topology, by Werner Ballmann, (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
I. First Steps in the Topology -- II. Manifolds -- III. Differential Forms and Cohomology -- IV. Geometry of Submanifolds -- A. Alternating Multilinear Forms -- B. Cochain Complexes -- Bibliography -- Index
Dimensions
unknown
Edition
1st ed. 2018.
Extent
1 online resource (X, 169 p. 28 illus., 20 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783034809832
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-0348-0983-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4100000005323336
  • (DE-He213)978-3-0348-0983-2
  • (EXLCZ)994100000005323336

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