Braids in trivial braid diagrams
几何拓扑
2007-05-23 v1
摘要
We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin--Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.
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引用
@article{arxiv.math/0311326,
title = {Braids in trivial braid diagrams},
author = {Patrick Dehornoy},
journal= {arXiv preprint arXiv:math/0311326},
year = {2007}
}