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Relations in singular
instanton homology
Peter B Kronheimer and Tomasz S Mrowka |
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Geometry & Topology 29 (2025) 1975–2046
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Abstract |
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We calculate the singular instanton homology with local coefficients for the simplest -strand braids in for all odd , describing these homology groups and their module structures in terms of the coordinate rings of explicit algebraic curves. The calculation is expected to be equivalent to computing the quantum cohomology ring of a certain Fano variety, namely a moduli space of stable parabolic bundles on a sphere with marked points. |
Keywords
instanton, Floer homology, parabolic bundle, quantum
cohomology, orbifold, representation variety
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Mathematical Subject Classification
Primary: 57R58
Secondary: 14H60
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References |
Publication
Received: 29 November 2022
Revised: 2 November 2023
Accepted: 17 December 2023
Published: 27 June 2025
Proposed: Simon Donaldson
Seconded: Martin R Bridson, Ian Agol
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Authors |
| Peter B Kronheimer | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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| Tomasz S Mrowka | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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