Multifraction reduction IV: Padding and Artin-Tits groups of sufficiently large type

Abstract

We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991, and connect it both with ordinary reduction and with the so-called Property $\mathrm{H}$. As an application, we show that all Artin-Tits groups of sufficiently large type satisfy some weakening Conjecture ${\mathrm{A}}^{\mathrm{padded}}$ of Conjecture $\mathrm{A}$, thus showing that the reduction approach is relevant for these groups.

18 pages

References in corpus (2)

• Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC
• Multifraction reduction II: Conjectures for Artin-Tits groups

Cited by in corpus (2)

• Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC
• Multifraction reduction II: Conjectures for Artin-Tits groups