We propose definitions of complex manifolds
that
could potentially be used to construct the symplectic Khovanov homology of
–stranded links in lens
spaces. The manifolds
are defined as moduli spaces of Hecke modifications of rank
parabolic bundles
over an elliptic curve
.
To characterize these spaces, we describe all possible Hecke modifications of all possible
rank
vector
bundles over
,
and we use these results to define a canonical open embedding of
into
, the moduli space of stable
rank
parabolic bundles over
with trivial determinant
bundle and
marked points.
We explicitly compute
for
.
For comparison, we present analogous results for the case of
rational curves, for which a corresponding complex manifold
is isomorphic
for
even to
a space
defined by Seidel and Smith that can be used to compute the symplectic Khovanov homology
of
–stranded
links in
.
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