Braid ordering and the geometry of closed braid

Abstract

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.

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

References in corpus (1)

• A new twist on Lorenz links

Cited by in corpus (4)

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