  The Kakimizu complex is usually defined in the context of knots, where it is
known to be quasi-Euclidean. We here generalize the definition of the Kakimizu
complex to surfaces and 3-manifolds (with or without boundary). Interestingly,
in the setting of surfaces, the complexes and the techniques turn out to
replicate those used to study the Torelli group, {\it i.e.,} the "nonlinear"
subgroup of the mapping class group. Our main results are that the Kakimizu
complexes of a surface are contractible and that they need not be
quasi-Euclidean. It follows that there exist (product) $3$-manifolds whose
Kakimizu complexes are not quasi-Euclidean.
