Logspace computations for Garside groups of spindle type

Abstract

M. Picantin introduced the notion of Garside groups of spindle type, generalizing the 3-strand braid group. We show that, for linear Garside groups of spindle type, a normal form and a solution to the conjugacy problem are logspace computable. For linear Garside groups of spindle type with homogenous presentation we compute a geodesic normal form in logspace.Comment: 22 pages; short version as v1. Terminolgy and title changed. In particular, in previous versions we called Garside groups of spindle type "rigid Garside groups