The Hauptvermutung Book: A Collection of Papers of the Topology of Manifolds
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
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| Schriftenreihe: | K-Monographs in Mathematics
1 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that further development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermutung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sullivan, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an introduction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc |
| Beschreibung: | 1 Online-Ressource (VI, 192 p) |
| ISBN: | 9789401733434 9789048147359 |
| ISSN: | 1386-2804 |
| DOI: | 10.1007/978-94-017-3343-4 |
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| 245 | 1 | 0 | |a The Hauptvermutung Book |b A Collection of Papers of the Topology of Manifolds |c by A. J. Casson, D. P. Sullivan, M. A. Armstrong, C. P. Rourke, G. E. Cooke ; edited by A. A. Ranicki |
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| 500 | |a The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that further development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermutung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sullivan, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an introduction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Cell aggregation / Mathematics | |
| 650 | 4 | |a Manifolds and Cell Complexes (incl. Diff.Topology) | |
| 650 | 4 | |a Algebraic Topology | |
| 650 | 4 | |a Global Analysis and Analysis on Manifolds | |
| 650 | 4 | |a Differential Geometry | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Casson, A. J. |
| author2 | Ranicki, A. A. |
| author2_role | edt |
| author2_variant | a a r aa aar |
| author_facet | Casson, A. J. Ranicki, A. A. |
| author_role | aut |
| author_sort | Casson, A. J. |
| author_variant | a j c aj ajc |
| building | Verbundindex |
| bvnumber | BV042424321 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)906704542 (DE-599)BVBBV042424321 |
| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.34 |
| dewey-search | 514.34 |
| dewey-sort | 3514.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-3343-4 |
| format | Electronic eBook |
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| id | DE-604.BV042424321 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401733434 9789048147359 |
| issn | 1386-2804 |
| language | English |
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| spelling | Casson, A. J. Verfasser aut The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds by A. J. Casson, D. P. Sullivan, M. A. Armstrong, C. P. Rourke, G. E. Cooke ; edited by A. A. Ranicki Dordrecht Springer Netherlands 1996 1 Online-Ressource (VI, 192 p) txt rdacontent c rdamedia cr rdacarrier K-Monographs in Mathematics 1 1386-2804 The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that further development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermutung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sullivan, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an introduction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc Mathematics Global analysis Geometry Global differential geometry Algebraic topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Algebraic Topology Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s 1\p DE-604 Sullivan, D. P. Sonstige oth Armstrong, M. A. Sonstige oth Rourke, C. P. Sonstige oth Cooke, G. E. Sonstige oth Ranicki, A. A. edt K-Monographs in Mathematics 1 (DE-604)BV011222840 1 https://doi.org/10.1007/978-94-017-3343-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Casson, A. J. The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds K-Monographs in Mathematics Mathematics Global analysis Geometry Global differential geometry Algebraic topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Algebraic Topology Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| subject_GND | (DE-588)4185712-4 |
| title | The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds |
| title_auth | The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds |
| title_exact_search | The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds |
| title_full | The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds by A. J. Casson, D. P. Sullivan, M. A. Armstrong, C. P. Rourke, G. E. Cooke ; edited by A. A. Ranicki |
| title_fullStr | The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds by A. J. Casson, D. P. Sullivan, M. A. Armstrong, C. P. Rourke, G. E. Cooke ; edited by A. A. Ranicki |
| title_full_unstemmed | The Hauptvermutung Book A Collection of Papers of the Topology of Manifolds by A. J. Casson, D. P. Sullivan, M. A. Armstrong, C. P. Rourke, G. E. Cooke ; edited by A. A. Ranicki |
| title_short | The Hauptvermutung Book |
| title_sort | the hauptvermutung book a collection of papers of the topology of manifolds |
| title_sub | A Collection of Papers of the Topology of Manifolds |
| topic | Mathematics Global analysis Geometry Global differential geometry Algebraic topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Algebraic Topology Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| topic_facet | Mathematics Global analysis Geometry Global differential geometry Algebraic topology Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Algebraic Topology Global Analysis and Analysis on Manifolds Differential Geometry Mathematik Topologische Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-94-017-3343-4 |
| volume_link | (DE-604)BV011222840 |
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