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A table of genus two handlebody-knots with seven crossings
Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini +1
We enumerate all genus two handlebody-knots with seven crossings, up to mirror image, extending the Ishii-Kishimoto-Moriuchi-Suzuki table.
Handlebody-knots obtained by tangle replacement
Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini +1
We study tangle replacement in the context of handlebody-knots. The main results classify the handlebody-knots obtained by performing tangle replacement on the prime spatial handcu…
On unique decomposition of knotted handlebodies
Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang
The paper considers the uniqueness question of factorization of a knotted handlebody in the -sphere along decomposing -spheres. We obtain a uniqueness result for factorizatio…
A table of -component handlebody links of genus up to six crossings
Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini +1
A handlebody link is a union of handlebodies of positive genus embedded in 3-space, which generalizes the notion of links in classical knot theory. In this paper, we consider handl…
Numerical irreducibility criteria for handlebody links
Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang
In this paper we define a set of numerical criteria for a handlebody link to be irreducible. It provides an effective, easy-to-implement method to determine the irreducibility of h…
A complete invariant for closed surfaces in the three-sphere
Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang
Associated to an embedded surface in the -sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, wherefrom we deduce complete invariant…