TY - JOUR
T1 - A complete invariant for closed surfaces in the three-sphere
AU - Bellettini, Giovanni
AU - Paolini, Maurizio
AU - Wang, Yi-Sheng
PY - 2021
Y1 - 2021
N2 - Associated to an embedded surface in the three-sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, whereform we deduce complete invariants of handlebody links, tunnels of handlebody links, and spatial graphs. The main ingredients in the proof of the completeness include a generalization of the Kneser conjecture for three-manifolds with boundary proved here, and extensions of Waldhausen's theorem by Evans, Tucker and Swarup. Computable invariants of handlebody links derived therefrom are calculated.
AB - Associated to an embedded surface in the three-sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, whereform we deduce complete invariants of handlebody links, tunnels of handlebody links, and spatial graphs. The main ingredients in the proof of the completeness include a generalization of the Kneser conjecture for three-manifolds with boundary proved here, and extensions of Waldhausen's theorem by Evans, Tucker and Swarup. Computable invariants of handlebody links derived therefrom are calculated.
KW - Kneser's conjecture
KW - Surfaces in three-space
KW - complete invariant
KW - Kneser's conjecture
KW - Surfaces in three-space
KW - complete invariant
UR - http://hdl.handle.net/10807/222065
U2 - 10.1142/S0218216521500449
DO - 10.1142/S0218216521500449
M3 - Article
SN - 0218-2165
VL - 30
SP - 1
EP - 25
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
ER -