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The 6-strand braid group is $$\mathrm{CAT}(0)$$. (English) Zbl 1347.20044
Summary: We show that braid groups with at most 6 strands are $$\mathrm{CAT}(0)$$ using the close connection between these groups, the associated non-crossing partition complexes, and the embeddability of their diagonal links into spherical buildings of type $$A$$. Furthermore, we prove that the orthoscheme complex of any bounded graded modular complemented lattice is $$\mathrm{CAT}(0)$$, giving a partial answer to a conjecture of Brady and McCammond.

##### MSC:
 20F65 Geometric group theory 20F36 Braid groups; Artin groups 20E42 Groups with a $$BN$$-pair; buildings 57M07 Topological methods in group theory
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##### References:
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