Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces
This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of the moduli space leads to interesting questions of a combinat...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209875 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces / S. Rayan // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 67 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719356904931328 |
|---|---|
| author | Rayan, S. |
| author_facet | Rayan, S. |
| citation_txt | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces / S. Rayan // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 67 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of the moduli space leads to interesting questions of a combinatorial nature.
|
| first_indexed | 2025-12-07T18:19:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209875 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:19:37Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rayan, S. 2025-11-28T09:38:21Z 2018 Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces / S. Rayan // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 67 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14D20; 46M20; 57N65; 05A19 arXiv: 1809.05732 https://nasplib.isofts.kiev.ua/handle/123456789/209875 https://doi.org/10.3842/SIGMA.2018.129 This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of the moduli space leads to interesting questions of a combinatorial nature. I thank Laura Schaposnik for organizing the series of workshops in which the mini-course took place, and both her and Lara Anderson for encouraging the preparation of this survey. With regards to the workshops, I acknowledge support from UIC NSF RTG Grant DMS-1246844, the UIC Start-Up Fund of L. Schaposnik, and the grants NSF DMS 1107452, 1107263, 1107367 RNMS: GEometric structures And Representation varieties (the GEAR Network). I am grateful to Marina Logares, who gave a mini-course in parallel to mine, for insightful discussions, as well as to Laura Fredrickson for useful comments on the manuscript during its preparation. I thank the referees for their helpful remarks and corrections that led to the final version of this article. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces Article published earlier |
| spellingShingle | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces Rayan, S. |
| title | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces |
| title_full | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces |
| title_fullStr | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces |
| title_full_unstemmed | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces |
| title_short | Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces |
| title_sort | aspects of the topology and combinatorics of higgs bundle moduli spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209875 |
| work_keys_str_mv | AT rayans aspectsofthetopologyandcombinatoricsofhiggsbundlemodulispaces |