The disk complex and topologically minimal surfaces in the 3-sphere
Mathematics and Statistics
Journal of Knot Theory and Its Ramifications
We show that the disk complex of a genus g > 1 Heegaard surface for the 3-sphere is homotopy equivalent to a wedge of (2g - 2)-dimensional spheres. This implies that genus g > 1 Heegaard surfaces for the 3-sphere are topologically minimal with index 2g - 1.
3-sphere, disk complex, Heegaard surfaces, Topologically minimal surfaces
Marion Campisi and Luis Torres. "The disk complex and topologically minimal surfaces in the 3-sphere" Journal of Knot Theory and Its Ramifications (2020). https://doi.org/10.1142/S0218216520500923