A complete invariant for closed surfaces in the three-sphere
Geometric Topology
2021-03-09 v2 Algebraic Topology
Abstract
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 invariants of handlebody links, tunnels of handlebody links, and spatial graphs.The main ingredients in the proof of the completeness are a generalization of the Kneser conjecture for -manifolds with boundary proved also here, and extensions of Waldhausen's theorem by Evans, Tucker and Swarup. Computable invariants of handlebody links derived therefrom are calculated.
Cite
@article{arxiv.1909.09328,
title = {A complete invariant for closed surfaces in the three-sphere},
author = {Giovanni Bellettini and Maurizio Paolini and Yi-Sheng Wang},
journal= {arXiv preprint arXiv:1909.09328},
year = {2021}
}
Comments
20 pages, 6 figures, proof of the main theorem simplified, following referee's report; section 6 restructured: Theorem 1.4 in v1 removed due to a gap in its proof; a new example added