Braid ordering and the geometry of closed braid

Details Braid ordering and the geometry of closed braid Braid ordering and the geometry of closed braid

2008-05-10

arxiv.org/abs/0805.1447v2

Geom. Topol. 15 (2011) 473-498

Mathematics

Geometric Topology

21 pages, 10 figures: Some figures are rewritten. Especially mistaken figure 2 is corrected

Scientific paper

10.2140/gt.2011.15.473

The relationships between braid ordering and the geometry of its closure is studied. We prove that if an essential closed surface $F$ in the complements of closed braid has relatively small genus with respect to the Dehornoy floor of the braid, $F$ is circular-foliated in a sense of Birman-Menasco's Braid foliation theory. As an application of the result, we prove that if Dehornoy floor of braids are larger than three, Nielsen-Thurston classification of braids and the geometry of their closure's complements are in one-to-one correspondence. Using this result, we construct infinitely many hyperbolic knots explicitly from pseudo-Anosov element of mapping class groups.

Affiliated with

Also associated with

No associations

Rating

Braid ordering and the geometry of closed braid does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Braid ordering and the geometry of closed braid, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Braid ordering and the geometry of closed braid will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-188622