Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles
The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recu...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1797055508907032576 |
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| author | Hausel, T Thaddeus, M |
| author_facet | Hausel, T Thaddeus, M |
| author_sort | Hausel, T |
| collection | OXFORD |
| description | The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the non-compact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance. Together, Parts I and II describe the cohomology rings of spaces of rank 2 Higgs bundles at essentially the same level of detail as is known for stable bundles. |
| first_indexed | 2024-03-06T19:11:40Z |
| format | Journal article |
| id | oxford-uuid:16fb9795-dc55-4409-96dc-48c577fd85c1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:11:40Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:16fb9795-dc55-4409-96dc-48c577fd85c12022-03-26T10:34:29ZRelations in the cohomology ring of the moduli space of rank 2 Higgs bundlesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:16fb9795-dc55-4409-96dc-48c577fd85c1EnglishSymplectic Elements at Oxford2000Hausel, TThaddeus, MThe moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the non-compact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance. Together, Parts I and II describe the cohomology rings of spaces of rank 2 Higgs bundles at essentially the same level of detail as is known for stable bundles. |
| spellingShingle | Hausel, T Thaddeus, M Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles |
| title | Relations in the cohomology ring of the moduli space of rank 2 Higgs
bundles |
| title_full | Relations in the cohomology ring of the moduli space of rank 2 Higgs
bundles |
| title_fullStr | Relations in the cohomology ring of the moduli space of rank 2 Higgs
bundles |
| title_full_unstemmed | Relations in the cohomology ring of the moduli space of rank 2 Higgs
bundles |
| title_short | Relations in the cohomology ring of the moduli space of rank 2 Higgs
bundles |
| title_sort | relations in the cohomology ring of the moduli space of rank 2 higgs bundles |
| work_keys_str_mv | AT hauselt relationsinthecohomologyringofthemodulispaceofrank2higgsbundles AT thaddeusm relationsinthecohomologyringofthemodulispaceofrank2higgsbundles |