Reducing spheres and weak reducing pairs for Heegaard surfaces in the 3-sphere

Key Points

• Non-separating weak reducing pairs allow for reducing spheres if the Heegaard surface has genus at most 3.
• A reducing sphere can separate the two disks of the weak reducing pair within the Heegaard surface context.
• The result indicates a relationship between the genus of Heegaard surfaces and the existence of certain reducing structures.
• This finding enhances understanding of topological properties of Heegaard surfaces within three-dimensional manifolds.