  Kakimizu complex of a knot is a flag simplicial complex whose vertices
correspond to minimal genus Seifert surfaces and edges to disjoint pairs of
such surfaces. We discuss a general setting in which one can define a similar
complex. We prove that this complex is contractible, which was conjectured by
Kakimizu. More generally, the fixed-point set (in the Kakimizu complex) for any
subgroup of an appropriate mapping class group is contractible or empty.
Moreover, we prove that this fixed-point set is non-empty for finite subgroups,
which implies the existence of symmetric Seifert surfaces.
