Geometriae Dedicata

, Volume 182, Issue 1, pp 263–286 | Cite as

The 6-strand braid group is CAT(0)

Original Paper

Abstract

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.

Keywords

Braid groups CAT(0) Non-crossing partitions Buildings Orthoscheme complexes Modular lattice 

Mathematics Subject Classification

20F65 20F36 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Institut Montpelliérain Alexander GrothendieckUniversité de MontpellierMontpellier Cedex 5France
  2. 2.Mathematisches InstitutUniversität BonnBonnGermany
  3. 3.Department of MathematicsKarlsruhe Institute of TechnologyKalrsruheGermany

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