A polynomial-time solution to the reducibility problem

Abstract

We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a reduction system of circles can be found completely if the input is a certain type of reducible braids.

13 pages, 7 figures

References in corpus (1)

• Some power of an element in a Garside group is conjugate to a periodically geodesic element

Cited by in corpus (1)

• A fast algorithm to the conjugacy problem on generic braids