General cycling operations in Garside groups
Abstract
Description
In this article, we introduce the notion of cycling operations of arbitrary order in Garside groups, which is a full generalization of the cycling and decycling operations. Theoretically, this notion together with other related concepts provides a context in which various definitions and arguments concerning Garside groups are unified and simplified as well as improved. Practically, it yields a new algorithm which has a considerably improved performance on solving the conjugacy problem of reducible braids.
22 pages. A new section (Section 7) was appended in the second version, in which we present several applications on the summit infimum/supremum, the stable summit set and the rigid elements
22 pages. A new section (Section 7) was appended in the second version, in which we present several applications on the summit infimum/supremum, the stable summit set and the rigid elements