MARC details
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05271nam a22004935i 4500 |
| 001 - CONTROL NUMBER |
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978-1-4612-4576-6 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20210602114659.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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110927s1988 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781461245766 |
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978-1-4612-4576-6 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-4612-4576-6 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA612-612.8 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBPD |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT038000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBPD |
| Source |
thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
514.2 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Rotman, Joseph J. |
| Relator term |
author. |
| Relator code |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 245 13 - TITLE STATEMENT |
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| Title |
An Introduction to Algebraic Topology |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Joseph J. Rotman. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1st ed. 1988. |
| 264 #1 - |
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New York, NY : |
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Springer New York : |
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Imprint: Springer, |
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1988. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XIV, 438 p. |
| Other physical details |
online resource. |
| 336 ## - |
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text |
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txt |
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rdacontent |
| 337 ## - |
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computer |
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c |
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rdamedia |
| 338 ## - |
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online resource |
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cr |
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rdacarrier |
| 347 ## - |
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text file |
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PDF |
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rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Graduate Texts in Mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume number/sequential designation |
119 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
0 Introduction -- Notation -- Brouwer Fixed Point Theorem -- Categories and Functors -- 1.Some Basic Topological Notions -- Homotopy -- Convexity, Contractibility, and Cones -- Paths and Path Connectedness -- 2 Simplexes -- Affine Spaces -- Affine Maps -- 3 The Fundamental Group -- The Fundamental Groupoid -- The Functor ?1 -- ?1(S1) -- 4 Singular Homology -- Holes and Green's Theorem -- Free Abelian Groups -- The Singular Complex and Homology Functors -- Dimension Axiom and Compact Supports -- The Homotopy Axiom -- The Hurewicz Theorem -- 5 Long Exact Sequences -- The Category Comp -- Exact Homology Sequences -- Reduced Homology -- 6 Excision and Applications -- Excision and Mayer-Vietoris -- Homology of Spheres and Some Applications -- Barycentric Subdivision and the Proof of Excision -- More Applications to Euclidean Space -- 7 Simplicial Complexes -- Definitions -- Simplicial Approximation -- Abstract Simplicial Complexes -- Simplicial Homology -- Comparison with Singular Homology -- Calculations -- Fundamental Groups of Polyhedra -- The Seifert-van Kampen Theorem -- 8 CW Complexes -- Hausdorff Quotient Spaces -- Attaching Cells -- Homology and Attaching Cells -- CW Complexes -- Cellular Homology -- 9 Natural Transformations -- Definitions and Examples -- Eilenberg-Steenrod Axioms -- Chain Equivalences -- Acyclic Models -- Lefschetz Fixed Point Theorem -- Tensor Products -- Universal Coefficients -- Eilenberg-Zilber Theorem and the Künneth Formula -- 10 Covering Spaces -- Basic Properties -- Covering Transformations -- Existence -- Orbit Spaces -- 11 Homotopy Groups -- Function Spaces -- Group Objects and Cogroup Objects -- Loop Space and Suspension -- Homotopy Groups -- Exact Sequences -- Fibrations -- A Glimpse Ahead -- 12 Cohomology -- Differential Forms -- Cohomology Groups -- Universal Coefficients Theorems for Cohomology -- Cohomology Rings -- Computations and Applications -- Notation. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. Whitehead. Of course, this is false, as a glance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details. There are two types of obstacle for the student learning algebraic topology. The first is the formidable array of new techniques (e. g. , most students know very little homological algebra); the second obstacle is that the basic defini tions have been so abstracted that their geometric or analytic origins have been obscured. I have tried to overcome these barriers. In the first instance, new definitions are introduced only when needed (e. g. , homology with coeffi cients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat-singular, sim plicial, and cellular). Moreover, many exercises are given to help the reader assimilate material. In the second instance, important definitions are often accompanied by an informal discussion describing their origins (e. g. , winding numbers are discussed before computing 1tl (Sl), Green's theorem occurs before defining homology, and differential forms appear before introducing cohomology). We assume that the reader has had a first course in point-set topology, but we do discuss quotient spaces, path connectedness, and function spaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebraic topology. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebraic Topology. |
| -- |
https://scigraph.springernature.com/ontologies/product-market-codes/M28019 |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781461289302 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9780387966786 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781461245773 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Graduate Texts in Mathematics, |
| -- |
0072-5285 ; |
| Volume number/sequential designation |
119 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-1-4612-4576-6">https://doi.org/10.1007/978-1-4612-4576-6</a> |
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ZDB-2-SMA |
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ZDB-2-SXMS |
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ZDB-2-BAE |
