An Introduction to Algebraic Topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1988
|
| Schriftenreihe: | Graduate Texts in Mathematics
119 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 definitions 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 coefficients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat- singular, simplicial, 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 |
| Beschreibung: | 1 Online-Ressource (XIV, 438 p) |
| ISBN: | 9781461245766 9781461289302 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-4576-6 |
Internformat
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| 245 | 1 | 0 | |a An Introduction to Algebraic Topology |c by Joseph J. Rotman |
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| 490 | 1 | |a Graduate Texts in Mathematics |v 119 |x 0072-5285 | |
| 500 | |a 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 definitions 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 coefficients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat- singular, simplicial, 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 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebraic topology | |
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Datensatz im Suchindex
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| author | Rotman, Joseph J. 1934- |
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| author_facet | Rotman, Joseph J. 1934- |
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| author_sort | Rotman, Joseph J. 1934- |
| author_variant | j j r jj jjr |
| building | Verbundindex |
| bvnumber | BV042420317 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863768514 (DE-599)BVBBV042420317 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4576-6 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461245766 9781461289302 |
| issn | 0072-5285 |
| language | English |
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| spelling | Rotman, Joseph J. 1934- Verfasser (DE-588)120676826 aut An Introduction to Algebraic Topology by Joseph J. Rotman New York, NY Springer New York 1988 1 Online-Ressource (XIV, 438 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 119 0072-5285 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 definitions 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 coefficients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat- singular, simplicial, 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 Mathematics Algebraic topology Algebraic Topology Mathematik Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s 1\p DE-604 Graduate Texts in Mathematics 119 (DE-604)BV035421258 119 https://doi.org/10.1007/978-1-4612-4576-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rotman, Joseph J. 1934- An Introduction to Algebraic Topology Graduate Texts in Mathematics Mathematics Algebraic topology Algebraic Topology Mathematik Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | An Introduction to Algebraic Topology |
| title_auth | An Introduction to Algebraic Topology |
| title_exact_search | An Introduction to Algebraic Topology |
| title_full | An Introduction to Algebraic Topology by Joseph J. Rotman |
| title_fullStr | An Introduction to Algebraic Topology by Joseph J. Rotman |
| title_full_unstemmed | An Introduction to Algebraic Topology by Joseph J. Rotman |
| title_short | An Introduction to Algebraic Topology |
| title_sort | an introduction to algebraic topology |
| topic | Mathematics Algebraic topology Algebraic Topology Mathematik Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Mathematics Algebraic topology Algebraic Topology Mathematik Algebraische Topologie |
| url | https://doi.org/10.1007/978-1-4612-4576-6 |
| volume_link | (DE-604)BV035421258 |
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