Fundamental Groups and Covering Spaces. (Record no. 67034)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04299nam a22004453i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3059502 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729124450.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2003 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781439864166 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781568811314 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3059502 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3059502 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr10159709 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)922955596 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA612 -- .L4713 2003eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 514/.2 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Lima, Elon Lages. |
| 245 10 - TITLE STATEMENT | |
| Title | Fundamental Groups and Covering Spaces. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Milton : |
| Name of producer, publisher, distributor, manufacturer | CRC Press LLC, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2003. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2003. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (221 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- I: Fundamental Groups -- 1: Homotopy -- 1.1 Homotopic Maps -- 1.1.1 Vector Fields on Spheres -- 1.2 Homotopy Type -- 1.3 Contractible Spaces -- 1.4 Homotopy and Map Extension -- 1.4.1 Euclidean Neighborhood Retracts -- 1.5 Trees -- 1.6 Homotopy of Pairs and Relative Homotopy -- 1.7 Exercises -- 2: The Fundamental Group -- 2.1 Path Homotopy -- 2.1.1 Operations with Paths -- 2.1.2 Homotopy and Path Decomposition -- 2.2 The Fundamental Group -- 2.3 The Induced Homomorphism -- 2.4 Other Descriptions of the Fundamental Group -- 2.4.1 Spaces with Abelian Fundamental Group -- 2.4.2 The Fundamental Group and Maps from S1 to X -- 2.5 Simply Connected Spaces -- 2.6 Some Properties of the Fundamental Group -- 2.7 Topological Groups -- 2.8 Exercises -- 3: Some Examples and Applications -- 3.1 The Fundamental Group of the Circle -- 3.2 The Isomorphism π(S1) ≈ Z -- 3.3 Real Projective Spaces -- 3.4 Fibrations and Complex Projective Spaces -- 3.5 Exercises -- 4: Classical Matrix Groups -- 4.1 Rotations in Euclidean Space -- 4.2 The Groups SU(n) and Sp(n) -- 4.3 Exercises -- 5: The Winding Number -- 5.1 The Winding Number of a Closed Plane Curve -- 5.2 The Graustein-Whitney Theorem -- 5.2.1 About Eversions -- 5.3 The Winding Number as a Curvilinear Integral -- 5.3.1 The Winding Number as a Complex Integral -- 5.4 Winding Number and Polynomial Roots -- 5.5 Exercises -- II: Covering Spaces -- 6: Covering Spaces -- 6.1 Local Homeomorphisms and Liftings -- 6.2 Covering Maps -- 6.3 Properly Discontinuous Groups -- 6.4 Path Lifting and Homotopies -- 6.4.1 An Application -- 6.5 Differentiable Coverings -- 6.6 Exercises -- 7: Covering Maps and Fundamental Groups -- 7.1 The Conjugate Class of a Covering Map -- 7.2 The Fundamental Lifting Theorem -- 7.3 Homomorphisms of Covering Spaces. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 7.4 Covering Automorphisms -- 7.5 Properly Discontinuous Groups and Regular Coverings -- 7.6 Existence of Coverings -- 7.7 Fundamental Group of a Compact Surface -- 7.8 Exercises -- 8: Oriented Double Covering -- 8.1 Orientation of a Vector Space -- 8.2 Orientable Manifolds -- 8.3 Properly Discontinuous Groups of Diffeomorphisms -- 8.4 Oriented Double Covering -- 8.5 Relations with the Fundamental Group -- 8.6 Exercises -- Appendix Proper Maps -- Bibliography -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This introductory textbook describes fundamental groups and their topological soul mates, the covering spaces. The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the books introductory aim, they are all quite elementary. Basic concepts are clearly defined, proofs are complete, and n. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Algebraic topology. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Lima, Elon Lages |
| Title | Fundamental Groups and Covering Spaces |
| Place, publisher, and date of publication | Milton : CRC Press LLC,c2003 |
| International Standard Book Number | 9781568811314 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3059502">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3059502</a> |
| Public note | Click to View |
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