Ends of complexes:
The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the relat...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1996
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| Schriftenreihe: | Cambridge tracts in mathematics
123 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour at infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xxv, 353 pages) |
| ISBN: | 9780511526299 |
| DOI: | 10.1017/CBO9780511526299 |
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| 100 | 1 | |a Hughes, Bruce |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ends of complexes |c Bruce Hughes, Andrew Ranicki |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a pt. 1. Topology at infinity. 1. End spaces. 2. Limits. 3. Homology at infinity. 4. Cellular homology. 5. Homology of covers. 6. Projective class and torsion. 7. Forward tameness. 8. Reverse tameness. 9. Homotopy at infinity. 10. Projective class at infinity. 11. Infinite torsion. 12. Forward tameness is a homotopy pushout -- pt. 2. Topology over the real line. 13. Infinite cyclic covers. 14. The mapping torus. 15. Geometric ribbons and bands. 16. Approximate fibrations. 17. Geometric wrapping up. 18. Geometric relaxation. 19. Homotopy theoretic twist glueing. 20. Homotopy theoretic wrapping up and relaxation -- pt. 3. The algebraic theory. 21. Polynomial extensions. 22. Algebraic bands. 23. Algebraic tameness. 24. Relaxation techniques. 25. Algebraic ribbons. 26. Algebraic twist glueing. 27. Wrapping up in algebraic K- and L-theory -- pt. 4. Appendices. Appendix A. Locally finite homology with local coefficient. Appendix B.A brief history of end spaces | |
| 520 | |a The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour at infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory | ||
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| 700 | 1 | |a Ranicki, Andrew |d 1948- |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804176884421885952 |
|---|---|
| any_adam_object | |
| author | Hughes, Bruce |
| author_facet | Hughes, Bruce |
| author_role | aut |
| author_sort | Hughes, Bruce |
| author_variant | b h bh |
| building | Verbundindex |
| bvnumber | BV043942028 |
| classification_rvk | SK 300 SK 350 |
| collection | ZDB-20-CBO |
| contents | pt. 1. Topology at infinity. 1. End spaces. 2. Limits. 3. Homology at infinity. 4. Cellular homology. 5. Homology of covers. 6. Projective class and torsion. 7. Forward tameness. 8. Reverse tameness. 9. Homotopy at infinity. 10. Projective class at infinity. 11. Infinite torsion. 12. Forward tameness is a homotopy pushout -- pt. 2. Topology over the real line. 13. Infinite cyclic covers. 14. The mapping torus. 15. Geometric ribbons and bands. 16. Approximate fibrations. 17. Geometric wrapping up. 18. Geometric relaxation. 19. Homotopy theoretic twist glueing. 20. Homotopy theoretic wrapping up and relaxation -- pt. 3. The algebraic theory. 21. Polynomial extensions. 22. Algebraic bands. 23. Algebraic tameness. 24. Relaxation techniques. 25. Algebraic ribbons. 26. Algebraic twist glueing. 27. Wrapping up in algebraic K- and L-theory -- pt. 4. Appendices. Appendix A. Locally finite homology with local coefficient. Appendix B.A brief history of end spaces |
| ctrlnum | (ZDB-20-CBO)CR9780511526299 (OCoLC)849972360 (DE-599)BVBBV043942028 |
| dewey-full | 514/.223 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.223 |
| dewey-search | 514/.223 |
| dewey-sort | 3514 3223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511526299 |
| format | Electronic eBook |
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| id | DE-604.BV043942028 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511526299 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350998 |
| oclc_num | 849972360 |
| open_access_boolean | |
| owner | DE-12 DE-355 DE-BY-UBR DE-92 |
| owner_facet | DE-12 DE-355 DE-BY-UBR DE-92 |
| physical | 1 online resource (xxv, 353 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR_PDA_CBO_Kauf |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Hughes, Bruce Verfasser aut Ends of complexes Bruce Hughes, Andrew Ranicki Cambridge Cambridge University Press 1996 1 online resource (xxv, 353 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 123 Title from publisher's bibliographic system (viewed on 05 Oct 2015) pt. 1. Topology at infinity. 1. End spaces. 2. Limits. 3. Homology at infinity. 4. Cellular homology. 5. Homology of covers. 6. Projective class and torsion. 7. Forward tameness. 8. Reverse tameness. 9. Homotopy at infinity. 10. Projective class at infinity. 11. Infinite torsion. 12. Forward tameness is a homotopy pushout -- pt. 2. Topology over the real line. 13. Infinite cyclic covers. 14. The mapping torus. 15. Geometric ribbons and bands. 16. Approximate fibrations. 17. Geometric wrapping up. 18. Geometric relaxation. 19. Homotopy theoretic twist glueing. 20. Homotopy theoretic wrapping up and relaxation -- pt. 3. The algebraic theory. 21. Polynomial extensions. 22. Algebraic bands. 23. Algebraic tameness. 24. Relaxation techniques. 25. Algebraic ribbons. 26. Algebraic twist glueing. 27. Wrapping up in algebraic K- and L-theory -- pt. 4. Appendices. Appendix A. Locally finite homology with local coefficient. Appendix B.A brief history of end spaces The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour at infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory Complexes Komplex Algebra (DE-588)4164880-8 gnd rswk-swf CW-Komplex (DE-588)4148419-8 gnd rswk-swf Komplex Algebra (DE-588)4164880-8 s 1\p DE-604 CW-Komplex (DE-588)4148419-8 s 2\p DE-604 Ranicki, Andrew 1948- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-05519-2 Erscheint auch als Druckausgabe 978-0-521-57625-3 https://doi.org/10.1017/CBO9780511526299 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hughes, Bruce Ends of complexes pt. 1. Topology at infinity. 1. End spaces. 2. Limits. 3. Homology at infinity. 4. Cellular homology. 5. Homology of covers. 6. Projective class and torsion. 7. Forward tameness. 8. Reverse tameness. 9. Homotopy at infinity. 10. Projective class at infinity. 11. Infinite torsion. 12. Forward tameness is a homotopy pushout -- pt. 2. Topology over the real line. 13. Infinite cyclic covers. 14. The mapping torus. 15. Geometric ribbons and bands. 16. Approximate fibrations. 17. Geometric wrapping up. 18. Geometric relaxation. 19. Homotopy theoretic twist glueing. 20. Homotopy theoretic wrapping up and relaxation -- pt. 3. The algebraic theory. 21. Polynomial extensions. 22. Algebraic bands. 23. Algebraic tameness. 24. Relaxation techniques. 25. Algebraic ribbons. 26. Algebraic twist glueing. 27. Wrapping up in algebraic K- and L-theory -- pt. 4. Appendices. Appendix A. Locally finite homology with local coefficient. Appendix B.A brief history of end spaces Complexes Komplex Algebra (DE-588)4164880-8 gnd CW-Komplex (DE-588)4148419-8 gnd |
| subject_GND | (DE-588)4164880-8 (DE-588)4148419-8 |
| title | Ends of complexes |
| title_auth | Ends of complexes |
| title_exact_search | Ends of complexes |
| title_full | Ends of complexes Bruce Hughes, Andrew Ranicki |
| title_fullStr | Ends of complexes Bruce Hughes, Andrew Ranicki |
| title_full_unstemmed | Ends of complexes Bruce Hughes, Andrew Ranicki |
| title_short | Ends of complexes |
| title_sort | ends of complexes |
| topic | Complexes Komplex Algebra (DE-588)4164880-8 gnd CW-Komplex (DE-588)4148419-8 gnd |
| topic_facet | Complexes Komplex Algebra CW-Komplex |
| url | https://doi.org/10.1017/CBO9780511526299 |
| work_keys_str_mv | AT hughesbruce endsofcomplexes AT ranickiandrew endsofcomplexes |