2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168560We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural choice, simplifying the algorithms concerning conjugacy in Garside groups and having nicer theoretical properties. We show, in particular, that if a super summit element has conjugates which are 'rigid' (that is, which have a certain particularly simple structure), then the optimal way of obtaining such a rigid conjugate through conjugation by positive elements is given by iterated cyclic sliding.28 pages. Updated reference, minor correctionGroup TheoryGeometric Topology20F36 (Primary) 20F10 (Secondary)text