General cycling operations in Garside groups

Details General cycling operations in Garside groups General cycling operations in Garside groups

2006-05-30

arxiv.org/abs/math/0605741v2

Mathematics

Geometric Topology

22 pages. A new section (Section 7) was appended in the second version, in which we present several applications on the summit

Scientific paper

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.

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