The disk complex and topologically minimal surfaces in the 3-sphere
Publication Date
12-1-2020
Document Type
Article
Publication Title
Journal of Knot Theory and Its Ramifications
Volume
29
Issue
14
DOI
10.1142/S0218216520500923
Abstract
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.
Keywords
3-sphere, disk complex, Heegaard surfaces, Topologically minimal surfaces
Department
Mathematics and Statistics
Recommended Citation
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
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