Braids in trivial braid diagrams

Details Braids in trivial braid diagrams Braids in trivial braid diagrams

2003-11-19

arxiv.org/abs/math/0311326v1

Topology 43-5 (2004) 1067-1079

Mathematics

Geometric Topology

Scientific paper

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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