Manifolds and Modular Forms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1994
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Aspects of Mathematics
20 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the A-genus. The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the A-genus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the A-genus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold |
| Beschreibung: | 1 Online-Ressource (XI, 212 p) |
| ISBN: | 9783663107262 9783528164140 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-663-10726-2 |
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Datensatz im Suchindex
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| author | Hirzebruch, Friedrich |
| author_facet | Hirzebruch, Friedrich |
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| author_sort | Hirzebruch, Friedrich |
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| dewey-full | 620 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620 |
| dewey-search | 620 |
| dewey-sort | 3620 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-663-10726-2 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042423558 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783663107262 9783528164140 |
| issn | 0179-2156 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858975 |
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| physical | 1 Online-Ressource (XI, 212 p) |
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| publishDate | 1994 |
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| publisher | Vieweg+Teubner Verlag |
| record_format | marc |
| series2 | Aspects of Mathematics |
| spelling | Hirzebruch, Friedrich Verfasser aut Manifolds and Modular Forms by Friedrich Hirzebruch, Thomas Berger, Rainer Jung Second Edition Wiesbaden Vieweg+Teubner Verlag 1994 1 Online-Ressource (XI, 212 p) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics 20 0179-2156 During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the A-genus. The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the A-genus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the A-genus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold Engineering Engineering, general Ingenieurwissenschaften Modulform (DE-588)4128299-1 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Elliptisches Geschlecht (DE-588)4318024-3 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Modulform (DE-588)4128299-1 s Elliptisches Geschlecht (DE-588)4318024-3 s 1\p DE-604 Komplexe Mannigfaltigkeit (DE-588)4031996-9 s 2\p DE-604 Berger, Thomas Sonstige oth Jung, Rainer Sonstige oth https://doi.org/10.1007/978-3-663-10726-2 Verlag 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 | Hirzebruch, Friedrich Manifolds and Modular Forms Engineering Engineering, general Ingenieurwissenschaften Modulform (DE-588)4128299-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Elliptisches Geschlecht (DE-588)4318024-3 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| subject_GND | (DE-588)4128299-1 (DE-588)4037379-4 (DE-588)4318024-3 (DE-588)4031996-9 |
| title | Manifolds and Modular Forms |
| title_auth | Manifolds and Modular Forms |
| title_exact_search | Manifolds and Modular Forms |
| title_full | Manifolds and Modular Forms by Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
| title_fullStr | Manifolds and Modular Forms by Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
| title_full_unstemmed | Manifolds and Modular Forms by Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
| title_short | Manifolds and Modular Forms |
| title_sort | manifolds and modular forms |
| topic | Engineering Engineering, general Ingenieurwissenschaften Modulform (DE-588)4128299-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Elliptisches Geschlecht (DE-588)4318024-3 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| topic_facet | Engineering Engineering, general Ingenieurwissenschaften Modulform Mannigfaltigkeit Elliptisches Geschlecht Komplexe Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-3-663-10726-2 |
| work_keys_str_mv | AT hirzebruchfriedrich manifoldsandmodularforms AT bergerthomas manifoldsandmodularforms AT jungrainer manifoldsandmodularforms |