We study the moduli space of rank holomorphic bundles with trivial determinant and second Chern class , over the blowup of the projective plane at points, trivialized on a rational curve. We show that, for , we have a homotopy equivalence between and the degree component of the bar construction . The space is isomorphic to the moduli space of charge based instantons on a connected sum of copies of and we show that, for , we have a homotopy equivalence between and the degree component of . Analogous results hold in the limit when . As an application we obtain upper bounds for the cokernel of the Atiyah–Jones map in homology, in the rank-stable limit.
"Holomorphic bundles on the blown-up plane and the bar construction." Algebr. Geom. Topol. 20 (5) 2177 - 2268, 2020. https://doi.org/10.2140/agt.2020.20.2177