Manifolds and Modular Forms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | German |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1992
|
| Schriftenreihe: | Aspects of Mathematics
E 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". Iwanted to develop the theory of "Elliptic Genera" and to leam 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 Thom 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 Chem 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 o 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 S.) |
| ISBN: | 9783663140450 9783528064143 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-663-14045-0 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042452255 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150324s1992 |||| o||u| ||||||ger d | ||
| 020 | |a 9783663140450 |c Online |9 978-3-663-14045-0 | ||
| 020 | |a 9783528064143 |c Print |9 978-3-528-06414-3 | ||
| 024 | 7 | |a 10.1007/978-3-663-14045-0 |2 doi | |
| 035 | |a (OCoLC)858044406 | ||
| 035 | |a (DE-599)BVBBV042452255 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a ger | |
| 049 | |a DE-91 |a DE-634 |a DE-92 |a DE-706 | ||
| 082 | 0 | |a 519 |2 23 | |
| 084 | |a NAT 000 |2 stub | ||
| 100 | 1 | |a Hirzebruch, Friedrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Manifolds and Modular Forms |c von Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
| 264 | 1 | |a Wiesbaden |b Vieweg+Teubner Verlag |c 1992 | |
| 300 | |a 1 Online-Ressource (XI, 212 S.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Aspects of Mathematics |v E 20 |x 0179-2156 | |
| 500 | |a During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". Iwanted to develop the theory of "Elliptic Genera" and to leam 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 Thom 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 Chem 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 o 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Popular Science in Mathematics/Computer Science/Natural Science/Technology | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Komplexe Mannigfaltigkeit |0 (DE-588)4031996-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mannigfaltigkeit |0 (DE-588)4037379-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modulform |0 (DE-588)4128299-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptisches Geschlecht |0 (DE-588)4318024-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mannigfaltigkeit |0 (DE-588)4037379-4 |D s |
| 689 | 0 | 1 | |a Modulform |0 (DE-588)4128299-1 |D s |
| 689 | 0 | 2 | |a Elliptisches Geschlecht |0 (DE-588)4318024-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Komplexe Mannigfaltigkeit |0 (DE-588)4031996-9 |D s |
| 689 | 1 | 1 | |a Modulform |0 (DE-588)4128299-1 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Berger, Thomas |e Sonstige |4 oth | |
| 700 | 1 | |a Jung, Rainer |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-663-14045-0 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SNA |a ZDB-2-BAD | ||
| 940 | 1 | |q ZDB-2-SNA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027887501 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153155978526720 |
|---|---|
| any_adam_object | |
| author | Hirzebruch, Friedrich |
| author_facet | Hirzebruch, Friedrich |
| author_role | aut |
| author_sort | Hirzebruch, Friedrich |
| author_variant | f h fh |
| building | Verbundindex |
| bvnumber | BV042452255 |
| classification_tum | NAT 000 |
| collection | ZDB-2-SNA ZDB-2-BAD |
| ctrlnum | (OCoLC)858044406 (DE-599)BVBBV042452255 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| doi_str_mv | 10.1007/978-3-663-14045-0 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03560nmm a2200601zcb4500</leader><controlfield tag="001">BV042452255</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150324s1992 |||| o||u| ||||||ger d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783663140450</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-663-14045-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783528064143</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-528-06414-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-663-14045-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)858044406</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042452255</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">NAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hirzebruch, Friedrich</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Manifolds and Modular Forms</subfield><subfield code="c">von Friedrich Hirzebruch, Thomas Berger, Rainer Jung</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Wiesbaden</subfield><subfield code="b">Vieweg+Teubner Verlag</subfield><subfield code="c">1992</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 212 S.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Aspects of Mathematics</subfield><subfield code="v">E 20</subfield><subfield code="x">0179-2156</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". Iwanted to develop the theory of "Elliptic Genera" and to leam 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 Thom 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 Chem 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 o 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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Applications of Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Popular Science in Mathematics/Computer Science/Natural Science/Technology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Komplexe Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4031996-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4037379-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Modulform</subfield><subfield code="0">(DE-588)4128299-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Elliptisches Geschlecht</subfield><subfield code="0">(DE-588)4318024-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4037379-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Modulform</subfield><subfield code="0">(DE-588)4128299-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Elliptisches Geschlecht</subfield><subfield code="0">(DE-588)4318024-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Komplexe Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4031996-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Modulform</subfield><subfield code="0">(DE-588)4128299-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Berger, Thomas</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jung, Rainer</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-663-14045-0</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SNA</subfield><subfield code="a">ZDB-2-BAD</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SNA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027887501</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042452255 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:22:07Z |
| institution | BVB |
| isbn | 9783663140450 9783528064143 |
| issn | 0179-2156 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027887501 |
| oclc_num | 858044406 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-634 DE-92 DE-706 |
| owner_facet | DE-91 DE-BY-TUM DE-634 DE-92 DE-706 |
| physical | 1 Online-Ressource (XI, 212 S.) |
| psigel | ZDB-2-SNA ZDB-2-BAD ZDB-2-SNA_Archive |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Vieweg+Teubner Verlag |
| record_format | marc |
| series2 | Aspects of Mathematics |
| spelling | Hirzebruch, Friedrich Verfasser aut Manifolds and Modular Forms von Friedrich Hirzebruch, Thomas Berger, Rainer Jung Wiesbaden Vieweg+Teubner Verlag 1992 1 Online-Ressource (XI, 212 S.) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics E 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". Iwanted to develop the theory of "Elliptic Genera" and to leam 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 Thom 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 Chem 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 o 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 Mathematics Applications of Mathematics Popular Science in Mathematics/Computer Science/Natural Science/Technology Mathematics, general Mathematik Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Elliptisches Geschlecht (DE-588)4318024-3 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/10.1007/978-3-663-14045-0 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 Mathematics Applications of Mathematics Popular Science in Mathematics/Computer Science/Natural Science/Technology Mathematics, general Mathematik Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Modulform (DE-588)4128299-1 gnd Elliptisches Geschlecht (DE-588)4318024-3 gnd |
| subject_GND | (DE-588)4031996-9 (DE-588)4037379-4 (DE-588)4128299-1 (DE-588)4318024-3 |
| title | Manifolds and Modular Forms |
| title_auth | Manifolds and Modular Forms |
| title_exact_search | Manifolds and Modular Forms |
| title_full | Manifolds and Modular Forms von Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
| title_fullStr | Manifolds and Modular Forms von Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
| title_full_unstemmed | Manifolds and Modular Forms von Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
| title_short | Manifolds and Modular Forms |
| title_sort | manifolds and modular forms |
| topic | Mathematics Applications of Mathematics Popular Science in Mathematics/Computer Science/Natural Science/Technology Mathematics, general Mathematik Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Modulform (DE-588)4128299-1 gnd Elliptisches Geschlecht (DE-588)4318024-3 gnd |
| topic_facet | Mathematics Applications of Mathematics Popular Science in Mathematics/Computer Science/Natural Science/Technology Mathematics, general Mathematik Komplexe Mannigfaltigkeit Mannigfaltigkeit Modulform Elliptisches Geschlecht |
| url | https://doi.org/10.1007/978-3-663-14045-0 |
| work_keys_str_mv | AT hirzebruchfriedrich manifoldsandmodularforms AT bergerthomas manifoldsandmodularforms AT jungrainer manifoldsandmodularforms |