For each integer
,
Mariño and Moore defined generalized Donaldson invariants by the methods of
quantum field theory, and made predictions about the values of these invariants.
Subsequently, Kronheimer gave a rigorous definition of generalized Donaldson invariants
using the moduli spaces of anti-self-dual connections on hermitian vector bundles of
rank
.
We confirm the predictions of Mariño and Moore for simply connected elliptic
surfaces without multiple fibers and certain surfaces of general type in the case that
. The primary motivation
is to study
–manifold
instanton Floer homologies which are defined by higher rank
bundles. In particular, the computation of the generalized Donaldson
invariants is exploited to define a Floer homology theory for sutured
–manifolds.
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