On the homology of 𝑆𝑈(𝑛) instantons

Abstract

In this paper we study the homology of the moduli spaces of instantons associated to principal S U ( n ) {\mathbf {SU}}(n) bundles over the four-sphere. This is accomplished by exploiting an "iterated loop space" structure implicit in the disjoint union of all moduli spaces associated to a fixed S U ( n ) {\mathbf {SU}}(n) with arbitrary instanton number and relating these spaces to the known homology structure of the four-fold loop space on B S U ( n ) B{\mathbf {SU}}(n) .