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.
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Centro de Análise Matemática,
Geometria e Sistemas Dinâmicos
Departamento de Matemática
Instituto Superior Técnico
Universidade de Lisboa
Lisboa
Portugal