Braid ordering and the geometry of closed braid

Ito, Tetsuya¹

¹ Graduate School of Mathematical Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku 153-8914, Japan

Geometry & topology, Tome 15 (2011) no. 1, pp. 473-498.

Résumé

We study the relationships between the Dehornoy ordering of the braid groups and the topology and geometry of the closed braid complements. We show that the Dehornoy floor of braids, which is a nonnegative integer determined by the Dehornoy ordering, tells us the position of essential surfaces in the closed braid complements. Furthermore, we prove that if the Dehornoy floor of a braid is bigger than or equal to two, then the Nielsen–Thurston classification of braids and the geometric structure of the closed braid complements are in one-to-one correspondence.

Détail

DOI : 10.2140/gt.2011.15.473

Keywords: braid group, Dehornoy ordering, Nielsen–Thurston classification, geometric structure

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