This paper proves a uniqueness result for 2-spheres that split a knotted handlebody in the 3-sphere along three parallel disks. We apply the result to study the symmetry of knotted handlebodies, measured by the mapping class group. In particular, the chirality of 610 in the handlebody-knot table, which was previously unknown, is determined. An infinite family of hyperbolic handlebody-knots with homeomorphic exteriors is also constructed.
Unique 3-decomposition and mapping classes of knotted handlebodies
Bellettini, Giovanni;
2025-01-01
Abstract
This paper proves a uniqueness result for 2-spheres that split a knotted handlebody in the 3-sphere along three parallel disks. We apply the result to study the symmetry of knotted handlebodies, measured by the mapping class group. In particular, the chirality of 610 in the handlebody-knot table, which was previously unknown, is determined. An infinite family of hyperbolic handlebody-knots with homeomorphic exteriors is also constructed.File in questo prodotto:
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