The disk complex and topologically minimal surfaces in the 3-sphere.
2019
We show that the disk complex of a closed, connected surface of genus $g>1$, properly embedded in the 3-sphere is homotopy equivalent to a wedge of $(2g-2)$-dimensional spheres. This implies that genus $g>1$ Heegaard surfaces of the 3-sphere are topologically minimal with index $2g-1$.
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