The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, N.J.
Princeton University Press
[1995]
|
| Series: | Mathematical Notes
44 |
| Subjects: | |
| Online Access: | UBM01 Volltext |
| Item Description: | The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces |
| Physical Description: | 1 Online-Ressource (130p.) |
| ISBN: | 9781400865161 |
| DOI: | 10.1515/9781400865161 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042524173 | ||
| 003 | DE-604 | ||
| 005 | 20220114 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150423s1995 |||| o||u| ||||||eng d | ||
| 020 | |a 9781400865161 |9 978-1-4008-6516-1 | ||
| 024 | 7 | |a 10.1515/9781400865161 |2 doi | |
| 035 | |a (OCoLC)891400523 | ||
| 035 | |a (DE-599)BVBBV042524173 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 | ||
| 082 | 0 | |a 514/.2 |2 23 | |
| 100 | 1 | |a Morgan, John W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |c John W. Morgan |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c [1995] | |
| 300 | |a 1 Online-Ressource (130p.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematical Notes |v 44 | |
| 500 | |a The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces | ||
| 546 | |a In English | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Four-manifolds (Topology) | |
| 650 | 4 | |a Seiberg-Witten invariants | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 7 | |a MATHEMATICS / Topology |2 bisacsh | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologische Mannigfaltigkeit |0 (DE-588)4185712-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differenzierbare Mannigfaltigkeit |0 (DE-588)4012269-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Seiberg-Witten-Invariante |0 (DE-588)4430370-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dimension 4 |0 (DE-588)4338676-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Topologische Mannigfaltigkeit |0 (DE-588)4185712-4 |D s |
| 689 | 0 | 1 | |a Dimension 4 |0 (DE-588)4338676-3 |D s |
| 689 | 0 | 2 | |a Seiberg-Witten-Invariante |0 (DE-588)4430370-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Differenzierbare Mannigfaltigkeit |0 (DE-588)4012269-4 |D s |
| 689 | 1 | 1 | |a Dimension 4 |0 (DE-588)4338676-3 |D s |
| 689 | 1 | 2 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400865161 |x Verlag |3 Volltext |
| 912 | |a ZDB-23-DGG | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027958512 | ||
| 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 | |
| 966 | e | |u https://doi.org/10.1515/9781400865161?locatt=mode:legacy |l UBM01 |p ZDB-23-DGG |q UBM_PDA_DGG_Kauf22 |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1804153278805573632 |
|---|---|
| any_adam_object | |
| author | Morgan, John W. |
| author_facet | Morgan, John W. |
| author_role | aut |
| author_sort | Morgan, John W. |
| author_variant | j w m jw jwm |
| building | Verbundindex |
| bvnumber | BV042524173 |
| collection | ZDB-23-DGG |
| ctrlnum | (OCoLC)891400523 (DE-599)BVBBV042524173 |
| dewey-full | 514/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400865161 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03753nmm a2200601zcb4500</leader><controlfield tag="001">BV042524173</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220114 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150423s1995 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400865161</subfield><subfield code="9">978-1-4008-6516-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400865161</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)891400523</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042524173</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">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514/.2</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Morgan, John W.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds</subfield><subfield code="c">John W. Morgan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, N.J.</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">[1995]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (130p.)</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">Mathematical Notes</subfield><subfield code="v">44</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Four-manifolds (Topology)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Seiberg-Witten invariants</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical physics</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Topology</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematische Physik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologische Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4185712-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differenzierbare Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4012269-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Seiberg-Witten-Invariante</subfield><subfield code="0">(DE-588)4430370-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dimension 4</subfield><subfield code="0">(DE-588)4338676-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Topologische Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4185712-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Dimension 4</subfield><subfield code="0">(DE-588)4338676-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Seiberg-Witten-Invariante</subfield><subfield code="0">(DE-588)4430370-1</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">Differenzierbare Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4012269-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Dimension 4</subfield><subfield code="0">(DE-588)4338676-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</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="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400865161</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027958512</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><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400865161?locatt=mode:legacy</subfield><subfield code="l">UBM01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UBM_PDA_DGG_Kauf22</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV042524173 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:04Z |
| institution | BVB |
| isbn | 9781400865161 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027958512 |
| oclc_num | 891400523 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM |
| owner_facet | DE-19 DE-BY-UBM |
| physical | 1 Online-Ressource (130p.) |
| psigel | ZDB-23-DGG ZDB-23-DGG UBM_PDA_DGG_Kauf22 |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Princeton University Press |
| record_format | marc |
| series2 | Mathematical Notes |
| spelling | Morgan, John W. Verfasser aut The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan Princeton, N.J. Princeton University Press [1995] 1 Online-Ressource (130p.) txt rdacontent c rdamedia cr rdacarrier Mathematical Notes 44 The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces In English Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Seiberg-Witten-Invariante (DE-588)4430370-1 gnd rswk-swf Dimension 4 (DE-588)4338676-3 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s Dimension 4 (DE-588)4338676-3 s Seiberg-Witten-Invariante (DE-588)4430370-1 s 1\p DE-604 Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s Mathematische Physik (DE-588)4037952-8 s 2\p DE-604 https://doi.org/10.1515/9781400865161 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 | Morgan, John W. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Seiberg-Witten-Invariante (DE-588)4430370-1 gnd Dimension 4 (DE-588)4338676-3 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4185712-4 (DE-588)4012269-4 (DE-588)4430370-1 (DE-588)4338676-3 |
| title | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_auth | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_exact_search | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_full | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan |
| title_fullStr | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan |
| title_full_unstemmed | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan |
| title_short | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_sort | the seiberg witten equations and applications to the topology of smooth four manifolds |
| topic | Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Seiberg-Witten-Invariante (DE-588)4430370-1 gnd Dimension 4 (DE-588)4338676-3 gnd |
| topic_facet | Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology Mathematische Physik Topologische Mannigfaltigkeit Differenzierbare Mannigfaltigkeit Seiberg-Witten-Invariante Dimension 4 |
| url | https://doi.org/10.1515/9781400865161 |
| work_keys_str_mv | AT morganjohnw theseibergwittenequationsandapplicationstothetopologyofsmoothfourmanifolds |