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.

Bellettini, G., Paolini, M., Wang, Y., A complete invariant for closed surfaces in the three-sphere, <<JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS>>, 2021; 30 (06): 1-25. [doi:10.1142/S0218216521500449] [https://hdl.handle.net/10807/222065]

A complete invariant for closed surfaces in the three-sphere

Paolini, Maurizio;
2021

Abstract

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.
Inglese
Bellettini, G., Paolini, M., Wang, Y., A complete invariant for closed surfaces in the three-sphere, <<JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS>>, 2021; 30 (06): 1-25. [doi:10.1142/S0218216521500449] [https://hdl.handle.net/10807/222065]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/222065
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