The Topology of CW Complexes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1969
|
| Schriftenreihe: | The University Series in Higher Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Most texts on algebraic topology emphasize homological algebra, with topological considerations limited to a few propositions about the geometry of simplicial complexes. There is much to be gained however, by using the more sophisticated concept of cell (CW) complex. Even for simple computations, this concept ordinarily allows us to bypass much tedious algebra and often gives geometric insight into the homology and homotopy theory of a space. For example, the easiest way to calculate and interpret the homology of Cpn, complex projective n-space, is by means of a cellular decomposition with only n+ 1 cells. Also, by a suitable construction we can "realize" the sin gular complex of a space as a CW complex and perhaps thus give a more geometric basis for some arguments involving singular homology theory for general spaces and a more concrete basis for singular ho motopy type. As a fInal example, if we start with the category of sim plicial complexes and maps, common topological constructions such as the formation of product spaces, identifIcation spaces, and adjunction spaces lead us often into the category of CW complexes. These topics, among others, are usually not treated thoroughly in a standard text, and the interested student must fInd them scattered through the literature. This book is a study of CW complexes. It is intended to supplement and be used concurrently with a standard text on algebraic topology |
| Beschreibung: | 1 Online-Ressource (VIII, 216 p.) 10 illus |
| ISBN: | 9781468462548 9781468462562 |
| DOI: | 10.1007/978-1-4684-6254-8 |
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| 245 | 1 | 0 | |a The Topology of CW Complexes |c by Albert T. Lundell, Stephen Weingram |
| 264 | 1 | |a New York, NY |b Springer New York |c 1969 | |
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| 490 | 0 | |a The University Series in Higher Mathematics | |
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Datensatz im Suchindex
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| ctrlnum | (OCoLC)863878684 (DE-599)BVBBV042421084 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-6254-8 |
| format | Electronic eBook |
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| id | DE-604.BV042421084 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468462548 9781468462562 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856501 |
| oclc_num | 863878684 |
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| physical | 1 Online-Ressource (VIII, 216 p.) 10 illus |
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| publishDate | 1969 |
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| publisher | Springer New York |
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| series2 | The University Series in Higher Mathematics |
| spelling | Lundell, Albert T. Verfasser aut The Topology of CW Complexes by Albert T. Lundell, Stephen Weingram New York, NY Springer New York 1969 1 Online-Ressource (VIII, 216 p.) 10 illus txt rdacontent c rdamedia cr rdacarrier The University Series in Higher Mathematics Most texts on algebraic topology emphasize homological algebra, with topological considerations limited to a few propositions about the geometry of simplicial complexes. There is much to be gained however, by using the more sophisticated concept of cell (CW) complex. Even for simple computations, this concept ordinarily allows us to bypass much tedious algebra and often gives geometric insight into the homology and homotopy theory of a space. For example, the easiest way to calculate and interpret the homology of Cpn, complex projective n-space, is by means of a cellular decomposition with only n+ 1 cells. Also, by a suitable construction we can "realize" the sin gular complex of a space as a CW complex and perhaps thus give a more geometric basis for some arguments involving singular homology theory for general spaces and a more concrete basis for singular ho motopy type. As a fInal example, if we start with the category of sim plicial complexes and maps, common topological constructions such as the formation of product spaces, identifIcation spaces, and adjunction spaces lead us often into the category of CW complexes. These topics, among others, are usually not treated thoroughly in a standard text, and the interested student must fInd them scattered through the literature. This book is a study of CW complexes. It is intended to supplement and be used concurrently with a standard text on algebraic topology Mathematics Mathematics, general Mathematik CW-Komplex (DE-588)4148419-8 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s CW-Komplex (DE-588)4148419-8 s 1\p DE-604 Weingram, Stephen Sonstige oth https://doi.org/10.1007/978-1-4684-6254-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lundell, Albert T. The Topology of CW Complexes Mathematics Mathematics, general Mathematik CW-Komplex (DE-588)4148419-8 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4148419-8 (DE-588)4060425-1 |
| title | The Topology of CW Complexes |
| title_auth | The Topology of CW Complexes |
| title_exact_search | The Topology of CW Complexes |
| title_full | The Topology of CW Complexes by Albert T. Lundell, Stephen Weingram |
| title_fullStr | The Topology of CW Complexes by Albert T. Lundell, Stephen Weingram |
| title_full_unstemmed | The Topology of CW Complexes by Albert T. Lundell, Stephen Weingram |
| title_short | The Topology of CW Complexes |
| title_sort | the topology of cw complexes |
| topic | Mathematics Mathematics, general Mathematik CW-Komplex (DE-588)4148419-8 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik CW-Komplex Topologie |
| url | https://doi.org/10.1007/978-1-4684-6254-8 |
| work_keys_str_mv | AT lundellalbertt thetopologyofcwcomplexes AT weingramstephen thetopologyofcwcomplexes |