The Resource An Introduction to Manifolds, by Loring W. Tu, (electronic resource)

An Introduction to Manifolds, by Loring W. Tu, (electronic resource)

Label
An Introduction to Manifolds
Title
An Introduction to Manifolds
Statement of responsibility
by Loring W. Tu
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology.
Member of
Is Subseries of
http://library.link/vocab/creatorName
Tu, Loring W
Dewey number
514.34
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
uxk2ifPkeUA
Language note
English
LC call number
  • QA613-613.8
  • QA613.6-613.66
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Cell aggregation
  • Global analysis (Mathematics)
  • Global differential geometry
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Global Analysis and Analysis on Manifolds
  • Differential Geometry
Label
An Introduction to Manifolds, by Loring W. Tu, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [347]) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Euclidean Spaces -- Smooth Functions on a Euclidean Space -- Tangent Vectors in Rn as Derivations -- Alternating k-Linear Functions -- Differential Forms on Rn -- Manifolds -- Manifolds -- Smooth Maps on a Manifold -- Quotients -- Lie Groups and Lie Algebras -- The Tangent Space -- Submanifolds -- Categories and Functors -- The Rank of a Smooth Map -- The Tangent Bundle -- Bump Functions and Partitions of Unity -- Vector Fields -- Lie Groups and Lie Algebras -- Lie Groups -- Lie Algebras -- Differential Forms -- Differential 1-Forms -- Differential k-Forms -- The Exterior Derivative -- Integration -- Orientations -- Manifolds with Boundary -- Integration on a Manifold -- De Rham Theory -- De Rham Cohomology -- The Long Exact Sequence in Cohomology -- The Mayer–Vietoris Sequence -- Homotopy Invariance -- Computation of de Rham Cohomology -- Proof of Homotopy Invariance
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (357 p.)
Form of item
online
Isbn
9780387481012
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-48101-2
Specific material designation
remote
System control number
  • (CKB)1000000000492017
  • (EBL)3062526
  • (SSID)ssj0000318484
  • (PQKBManifestationID)11241986
  • (PQKBTitleCode)TC0000318484
  • (PQKBWorkID)10310956
  • (PQKB)10410057
  • (DE-He213)978-0-387-48101-2
  • (MiAaPQ)EBC3062526
  • (EXLCZ)991000000000492017
Label
An Introduction to Manifolds, by Loring W. Tu, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [347]) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Euclidean Spaces -- Smooth Functions on a Euclidean Space -- Tangent Vectors in Rn as Derivations -- Alternating k-Linear Functions -- Differential Forms on Rn -- Manifolds -- Manifolds -- Smooth Maps on a Manifold -- Quotients -- Lie Groups and Lie Algebras -- The Tangent Space -- Submanifolds -- Categories and Functors -- The Rank of a Smooth Map -- The Tangent Bundle -- Bump Functions and Partitions of Unity -- Vector Fields -- Lie Groups and Lie Algebras -- Lie Groups -- Lie Algebras -- Differential Forms -- Differential 1-Forms -- Differential k-Forms -- The Exterior Derivative -- Integration -- Orientations -- Manifolds with Boundary -- Integration on a Manifold -- De Rham Theory -- De Rham Cohomology -- The Long Exact Sequence in Cohomology -- The Mayer–Vietoris Sequence -- Homotopy Invariance -- Computation of de Rham Cohomology -- Proof of Homotopy Invariance
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (357 p.)
Form of item
online
Isbn
9780387481012
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-48101-2
Specific material designation
remote
System control number
  • (CKB)1000000000492017
  • (EBL)3062526
  • (SSID)ssj0000318484
  • (PQKBManifestationID)11241986
  • (PQKBTitleCode)TC0000318484
  • (PQKBWorkID)10310956
  • (PQKB)10410057
  • (DE-He213)978-0-387-48101-2
  • (MiAaPQ)EBC3062526
  • (EXLCZ)991000000000492017

Library Locations

  • Albert D. Cohen Management LibraryBorrow it
    181 Freedman Crescent, Winnipeg, MB, R3T 5V4, CA
    49.807878 -97.129961
  • Architecture/Fine Arts LibraryBorrow it
    84 Curry Place, Winnipeg, MB, CA
    49.807716 -97.136226
  • Archives and Special CollectionsBorrow it
    25 Chancellors Circle (Elizabeth Dafoe Library), Room 330, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Bibliothèque Alfred-Monnin (Université de Saint-Boniface)Borrow it
    200, avenue de la Cathédrale, Local 2110, Winnipeg, MB, R2H 0H7, CA
    49.888861 -97.119735
  • Bill Larson Library (Grace Hospital)Borrow it
    300 Booth Drive, G-227, Winnipeg, MB, R3J 3M7, CA
    49.882400 -97.276436
  • Carolyn Sifton - Helene Fuld Library (St. Boniface General Hospital)Borrow it
    409 Tache Avenue, Winnipeg, MB, R2H 2A6, CA
    49.883388 -97.126050
  • Concordia Hospital LibraryBorrow it
    1095 Concordia Avenue, Winnipeg, MB, R2K 3S8, CA
    49.913252 -97.064683
  • Donald W. Craik Engineering LibraryBorrow it
    75B Chancellors Circle (Engineering Building E3), Room 361, Winnipeg, MB, R3T 2N2, CA
    49.809053 -97.133292
  • E.K. Williams Law LibraryBorrow it
    224 Dysart Road, Winnipeg, MB, R3T 5V4, CA
    49.811829 -97.131017
  • Eckhardt-Gramatté Music LibraryBorrow it
    136 Dafoe Road (Taché Arts Complex), Room 257, Winnipeg, MB, R3T 2N2, CA
    49.807964 -97.132222
  • Elizabeth Dafoe LibraryBorrow it
    25 Chancellors Circle, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Fr. H. Drake Library (St. Paul's College)Borrow it
    70 Dysart Road, Winnipeg, MB, R3T 2M6, CA
    49.810605 -97.138184
  • J.W. Crane Memorial Library (Deer Lodge Centre)Borrow it
    2109 Portage Avenue, Winnipeg, MB, R3J 0L3, CA
    49.878000 -97.235520
  • Libraries Annex (not open to the public; please see web page for details)Borrow it
    25 Chancellors Circle (in the Elizabeth Dafoe Library), Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Neil John Maclean Health Sciences LibraryBorrow it
    727 McDermot Avenue (Brodie Centre), 200 Level, Winnipeg, MB, R3E 3P5, CA
    49.903563 -97.160554
  • Sciences and Technology LibraryBorrow it
    186 Dysart Road, Winnipeg, MB, R3T 2M8, CA
    49.811526 -97.133257
  • Seven Oaks General Hospital LibraryBorrow it
    2300 McPhillips Street, Winnipeg, MB, R2V 3M3, CA
    49.955177 -97.148865
  • Sister St. Odilon Library (Misericordia Health Centre)Borrow it
    99 Cornish Avenue, Winnipeg, MB, R3C 1A2, CA
    49.879592 -97.160425
  • St. John's College LibraryBorrow it
    92 Dysart Road, Winnipeg, MB, R3T 2M5, CA
    49.811242 -97.137156
  • Victoria General Hospital LibraryBorrow it
    2340 Pembina Highway, Winnipeg, MB, R3T 2E8, CA
    49.806755 -97.152739
  • William R Newman Library (Agriculture)Borrow it
    66 Dafoe Road, Winnipeg, MB, R3T 2R3, CA
    49.806936 -97.135525
Processing Feedback ...