TY - JOUR
T1 - A complete invariant for connected surfaces in the 3-sphere
AU - Bellettini, Giovanni
AU - Paolini, Maurizio
AU - Wang, Yi-Sheng
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Complete invariant
KW - Handlebody knots
KW - Surfaces in the 3-sphere
KW - Complete invariant
KW - Handlebody knots
KW - Surfaces in the 3-sphere
UR - http://hdl.handle.net/10807/164839
U2 - 10.1142/S0218216519500913
DO - 10.1142/S0218216519500913
M3 - Article
SN - 0218-2165
VL - 29
SP - 1
EP - 24
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
ER -