Relations in singular instanton homology

Kronheimer, Peter B¹ ; Mrowka, Tomasz S²

¹Department of Mathematics, Harvard University, Cambridge, MA, United States
²Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States

Geometry & topology, Tome 29 (2025) no. 4, pp. 1975-2046

Résumé

We calculate the singular instanton homology with local coefficients for the simplest n-strand braids in S1 × S2 for all odd n, 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 n marked points.

Détail

DOI : 10.2140/gt.2025.29.1975

Keywords: instanton, Floer homology, parabolic bundle, quantum cohomology, orbifold, representation variety

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