The disk complex and topologically minimal surfaces in the 3-sphere.

We show that the disk complex of a genus g > 1 Heegaard surface for the 3-sphere is homotopy equivalent to a wedge of (2 g − 2) -dimensional spheres. This implies that genus g > 1 Heegaard surfaces for the 3-sphere are topologically minimal with index 2 g − 1. [ABSTRACT FROM AUTHOR]