Introduction to Combinatorial Torsions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2001
|
| Schriftenreihe: | Lectures in Mathematics ETH Zürich, Department of Mathematics Research Institute of Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is an extended version of the notes of my lecture course given at ETH in spring 1999. The course was intended as an introduction to combinatorial torsions and their relations to the famous Seiberg-Witten invariants. Torsions were introduced originally in the 3-dimensional setting by K. Rei demeister (1935) who used them to give a homeomorphism classification of 3-dimensional lens spaces. The Reidemeister torsions are defined using simple linear algebra and standard notions of combinatorial topology: triangulations (or, more generally, CW-decompositions), coverings, cellular chain complexes, etc. The Reidemeister torsions were generalized to arbitrary dimensions by W. Franz (1935) and later studied by many authors. In 1962, J. Milnor observed 3 that the classical Alexander polynomial of a link in the 3-sphere 8 can be interpreted as a torsion of the link exterior. Milnor's arguments work for an arbitrary compact 3-manifold M whose boundary is non-void and consists of tori: The Alexander polynomial of M and the Milnor torsion of M essentially coincide |
| Beschreibung: | 1 Online-Ressource (VIII, 123p) |
| ISBN: | 9783034883214 9783764364038 |
| DOI: | 10.1007/978-3-0348-8321-4 |
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8321-4 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034883214 9783764364038 |
| language | English |
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| spelling | Turaev, Vladimir Verfasser aut Introduction to Combinatorial Torsions by Vladimir Turaev Basel Birkhäuser Basel 2001 1 Online-Ressource (VIII, 123p) txt rdacontent c rdamedia cr rdacarrier Lectures in Mathematics ETH Zürich, Department of Mathematics Research Institute of Mathematics This book is an extended version of the notes of my lecture course given at ETH in spring 1999. The course was intended as an introduction to combinatorial torsions and their relations to the famous Seiberg-Witten invariants. Torsions were introduced originally in the 3-dimensional setting by K. Rei demeister (1935) who used them to give a homeomorphism classification of 3-dimensional lens spaces. The Reidemeister torsions are defined using simple linear algebra and standard notions of combinatorial topology: triangulations (or, more generally, CW-decompositions), coverings, cellular chain complexes, etc. The Reidemeister torsions were generalized to arbitrary dimensions by W. Franz (1935) and later studied by many authors. In 1962, J. Milnor observed 3 that the classical Alexander polynomial of a link in the 3-sphere 8 can be interpreted as a torsion of the link exterior. Milnor's arguments work for an arbitrary compact 3-manifold M whose boundary is non-void and consists of tori: The Alexander polynomial of M and the Milnor torsion of M essentially coincide Mathematics Mathematics, general Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Torsionstheorie (DE-588)4451084-6 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Torsionstheorie (DE-588)4451084-6 s Homologietheorie (DE-588)4141714-8 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8321-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Turaev, Vladimir Introduction to Combinatorial Torsions Mathematics Mathematics, general Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd Homologietheorie (DE-588)4141714-8 gnd Torsionstheorie (DE-588)4451084-6 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4141714-8 (DE-588)4451084-6 |
| title | Introduction to Combinatorial Torsions |
| title_auth | Introduction to Combinatorial Torsions |
| title_exact_search | Introduction to Combinatorial Torsions |
| title_full | Introduction to Combinatorial Torsions by Vladimir Turaev |
| title_fullStr | Introduction to Combinatorial Torsions by Vladimir Turaev |
| title_full_unstemmed | Introduction to Combinatorial Torsions by Vladimir Turaev |
| title_short | Introduction to Combinatorial Torsions |
| title_sort | introduction to combinatorial torsions |
| topic | Mathematics Mathematics, general Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd Homologietheorie (DE-588)4141714-8 gnd Torsionstheorie (DE-588)4451084-6 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Mannigfaltigkeit Homologietheorie Torsionstheorie |
| url | https://doi.org/10.1007/978-3-0348-8321-4 |
| work_keys_str_mv | AT turaevvladimir introductiontocombinatorialtorsions |