We construct a complete invariant of oriented connected closed surfaces in 3, which generalizes the notion of peripheral system of a knot group. As an application, we define two computable invariants to investigate handlebody knots and bi-knotted surfaces with homeomorphic complements. In particular, we obtain an alternative proof of inequivalence of Ishii, Kishimoto, Moriuchi and Suzuki's handlebody knots 51 and 64.
Bellettini, G., Paolini, M., Wang, Y. -., A complete invariant for connected surfaces in the 3-sphere, <<JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS>>, 2020; 29 (1): 1-24. [doi:10.1142/S0218216519500913] [http://hdl.handle.net/10807/164839]
A complete invariant for connected surfaces in the 3-sphere
Paolini, Maurizio;
2020
Abstract
We construct a complete invariant of oriented connected closed surfaces in 3, which generalizes the notion of peripheral system of a knot group. As an application, we define two computable invariants to investigate handlebody knots and bi-knotted surfaces with homeomorphic complements. In particular, we obtain an alternative proof of inequivalence of Ishii, Kishimoto, Moriuchi and Suzuki's handlebody knots 51 and 64.
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