Fast algorithmic Nielsen-Thurston classification of four-strand braids

Matthieu Calvez; Bert Wiest

Fast algorithmic Nielsen-Thurston classification of four-strand braids

Group Theory 2015-03-13 v4

Authors: Matthieu Calvez , Bert Wiest

Abstract

We give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid. The complexity of our algorithm is quadratic with respect to word length. The proof of its validity is based on a result which states that for a reducible 4-braid which is as short as possible within its conjugacy class (short in the sense of Garside), reducing curves surrounding three punctures must be round or almost round.

Keywords

nielsen-thurston classification braid groups garside normal form reducible braids algorithmic complexity four-strand braids

Cite

@article{arxiv.1004.0067,
  title  = {Fast algorithmic Nielsen-Thurston classification of four-strand braids},
  author = {Matthieu Calvez and Bert Wiest},
  journal= {arXiv preprint arXiv:1004.0067},
  year   = {2015}
}

Comments

One minor error corrected (Example 4.2 was wrong)

Fast algorithmic Nielsen-Thurston classification of four-strand braids

Abstract

Keywords

Cite

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