Torsions of 3-dimensional Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2002
|
| Schriftenreihe: | Progress in Mathematics
208 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Three-dimensional topology includes two vast domains: the study of geometric structures on 3-manifolds and the study of topological invariants of 3-manifolds, knots, etc. This book belongs to the second domain. We shall study an invariant called the maximal abelian torsion and denoted T. It is defined for a compact smooth (or piecewise-linear) manifold of any dimension and, more generally, for an arbitrary finite CW-complex X. The torsion T(X) is an element of a certain extension of the group ring Z[Hl(X)]. The torsion T can be naturally considered in the framework of simple homotopy theory. In particular, it is invariant under simple homotopy equivalences and can distinguish homotopy equivalent but non homeomorphic CW-spaces and manifolds, for instance, lens spaces. The torsion T can be used also to distinguish orientations and so-called Euler structures. Our interest in the torsion T is due to a particular role which it plays in three-dimensional topology. First of all, it is intimately related to a number of fundamental topological invariants of 3-manifolds. The torsion T(M) of a closed oriented 3-manifold M dominates (determines) the first elementary ideal of 7fl (M) and the Alexander polynomial of 7fl (M). The torsion T(M) is closely related to the cohomology rings of M with coefficients in Z and ZjrZ (r ;::: 2). It is also related to the linking form on Tors Hi (M), to the Massey products in the cohomology of M, and to the Thurston norm on H2(M) |
| Beschreibung: | 1 Online-Ressource (X, 196 p) |
| ISBN: | 9783034879996 9783034893985 |
| DOI: | 10.1007/978-3-0348-7999-6 |
Internformat
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| 500 | |a Three-dimensional topology includes two vast domains: the study of geometric structures on 3-manifolds and the study of topological invariants of 3-manifolds, knots, etc. This book belongs to the second domain. We shall study an invariant called the maximal abelian torsion and denoted T. It is defined for a compact smooth (or piecewise-linear) manifold of any dimension and, more generally, for an arbitrary finite CW-complex X. The torsion T(X) is an element of a certain extension of the group ring Z[Hl(X)]. The torsion T can be naturally considered in the framework of simple homotopy theory. In particular, it is invariant under simple homotopy equivalences and can distinguish homotopy equivalent but non homeomorphic CW-spaces and manifolds, for instance, lens spaces. The torsion T can be used also to distinguish orientations and so-called Euler structures. Our interest in the torsion T is due to a particular role which it plays in three-dimensional topology. First of all, it is intimately related to a number of fundamental topological invariants of 3-manifolds. The torsion T(M) of a closed oriented 3-manifold M dominates (determines) the first elementary ideal of 7fl (M) and the Alexander polynomial of 7fl (M). The torsion T(M) is closely related to the cohomology rings of M with coefficients in Z and ZjrZ (r ;::: 2). It is also related to the linking form on Tors Hi (M), to the Massey products in the cohomology of M, and to the Thurston norm on H2(M) | ||
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Datensatz im Suchindex
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| author | Turaev, Vladimir |
| author_facet | Turaev, Vladimir |
| author_role | aut |
| author_sort | Turaev, Vladimir |
| author_variant | v t vt |
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| dewey-full | 514.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7999-6 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034879996 9783034893985 |
| language | English |
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| spelling | Turaev, Vladimir Verfasser aut Torsions of 3-dimensional Manifolds by Vladimir Turaev Basel Birkhäuser Basel 2002 1 Online-Ressource (X, 196 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 208 Three-dimensional topology includes two vast domains: the study of geometric structures on 3-manifolds and the study of topological invariants of 3-manifolds, knots, etc. This book belongs to the second domain. We shall study an invariant called the maximal abelian torsion and denoted T. It is defined for a compact smooth (or piecewise-linear) manifold of any dimension and, more generally, for an arbitrary finite CW-complex X. The torsion T(X) is an element of a certain extension of the group ring Z[Hl(X)]. The torsion T can be naturally considered in the framework of simple homotopy theory. In particular, it is invariant under simple homotopy equivalences and can distinguish homotopy equivalent but non homeomorphic CW-spaces and manifolds, for instance, lens spaces. The torsion T can be used also to distinguish orientations and so-called Euler structures. Our interest in the torsion T is due to a particular role which it plays in three-dimensional topology. First of all, it is intimately related to a number of fundamental topological invariants of 3-manifolds. The torsion T(M) of a closed oriented 3-manifold M dominates (determines) the first elementary ideal of 7fl (M) and the Alexander polynomial of 7fl (M). The torsion T(M) is closely related to the cohomology rings of M with coefficients in Z and ZjrZ (r ;::: 2). It is also related to the linking form on Tors Hi (M), to the Massey products in the cohomology of M, and to the Thurston norm on H2(M) Mathematics Global analysis Topology Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Topologische Invariante (DE-588)4310559-2 gnd rswk-swf Torsion Mathematik (DE-588)4627078-4 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Topologische Invariante (DE-588)4310559-2 s Torsion Mathematik (DE-588)4627078-4 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-7999-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Turaev, Vladimir Torsions of 3-dimensional Manifolds Mathematics Global analysis Topology Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd Topologische Invariante (DE-588)4310559-2 gnd Torsion Mathematik (DE-588)4627078-4 gnd Dimension 3 (DE-588)4321722-9 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4310559-2 (DE-588)4627078-4 (DE-588)4321722-9 |
| title | Torsions of 3-dimensional Manifolds |
| title_auth | Torsions of 3-dimensional Manifolds |
| title_exact_search | Torsions of 3-dimensional Manifolds |
| title_full | Torsions of 3-dimensional Manifolds by Vladimir Turaev |
| title_fullStr | Torsions of 3-dimensional Manifolds by Vladimir Turaev |
| title_full_unstemmed | Torsions of 3-dimensional Manifolds by Vladimir Turaev |
| title_short | Torsions of 3-dimensional Manifolds |
| title_sort | torsions of 3 dimensional manifolds |
| topic | Mathematics Global analysis Topology Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd Topologische Invariante (DE-588)4310559-2 gnd Torsion Mathematik (DE-588)4627078-4 gnd Dimension 3 (DE-588)4321722-9 gnd |
| topic_facet | Mathematics Global analysis Topology Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Mannigfaltigkeit Topologische Invariante Torsion Mathematik Dimension 3 |
| url | https://doi.org/10.1007/978-3-0348-7999-6 |
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