The Kakimizu complex of a surface

We introduce a complex that encodes isotopy classes of curves
representing a primitive homology class.
The complex, called the Kakimizu complex of a surface, is inspired by its 3-dimensional analogue, the Kakimizu complex of a 3-manifold.  We will discuss its relation to the cyclic cycle complex defined by A. Hatcher and the homology curve complex defined by I. Irmer.  Several results on the Kakimizu complex of a 3-manifold carry over to the setting of the Kakimizu complex of a surface.  Conversely, results on the Kakimizu complex of a surface can be `lifted' to the setting of the Kakimizu complex of a 3-manifold via product constructions.