Lectures on Algebraic Topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1972
|
| Series: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
200 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applications of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions |
| Physical Description: | 1 Online-Ressource (XI, 380 p) |
| ISBN: | 9783662007563 9783662007587 |
| DOI: | 10.1007/978-3-662-00756-3 |
Staff View
MARC
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| 490 | 1 | |a Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |v 200 | |
| 500 | |a This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applications of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebraic topology | |
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Record in the Search Index
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| author | Dold, Albrecht 1928-2011 |
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| 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 | 10.1007/978-3-662-00756-3 |
| format | Electronic eBook |
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| id | DE-604.BV042423182 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:38:45Z |
| institution | BVB |
| isbn | 9783662007563 9783662007587 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858599 |
| oclc_num | 863949113 |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XI, 380 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| series2 | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Dold, Albrecht 1928-2011 Verfasser (DE-588)117709549 aut Lectures on Algebraic Topology by Albrecht Dold Berlin, Heidelberg Springer Berlin Heidelberg 1972 1 Online-Ressource (XI, 380 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 200 This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applications of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions 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 Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 200 (DE-604)BV049758308 200 https://doi.org/10.1007/978-3-662-00756-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dold, Albrecht 1928-2011 Lectures on Algebraic Topology Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete Mathematics Algebraic topology Algebraic Topology Mathematik Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Lectures on Algebraic Topology |
| title_auth | Lectures on Algebraic Topology |
| title_exact_search | Lectures on Algebraic Topology |
| title_full | Lectures on Algebraic Topology by Albrecht Dold |
| title_fullStr | Lectures on Algebraic Topology by Albrecht Dold |
| title_full_unstemmed | Lectures on Algebraic Topology by Albrecht Dold |
| title_short | Lectures on Algebraic Topology |
| title_sort | lectures on 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/10.1007/978-3-662-00756-3 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT doldalbrecht lecturesonalgebraictopology |