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
Main Author: Rayan, S.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
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
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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
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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