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The 6-strand braid group is CAT(0)

We show that braid groups with at most 6 strands are 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 CAT(0), giving a partial answer to a conjecture of Brady and McCammond.

preprint2016arXivOpen access
Thomas HaettelDawid KielakPetra Schwer
math.COmath.GR
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Thomas HaettelDawid KielakPetra Schwer

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