23 citations · 257 across the 67 of their papers we have counts for
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math.GR2008★ 5 cited
On finite Thurston type orderings of braid groups
Tetsuya Ito
We prove that for any finite Thurston-type ordering on the braid group\ , the restriction to the positive braid monoid is a\ well-ordered set of…
math.GT2008★ 3 cited
Braid ordering and knot genus
Tetsuya Ito
The genus of knots is a one of the fundamental invariant and can be seen as a complexity of knots. In this paper, we give a lower bound of genus using Dehornoy floor, which is a me…
math.GT2008★ 18 cited
Braid ordering and the geometry of closed braid
Tetsuya Ito
The relationships between braid ordering and the geometry of its closure is studied. We prove that if an essential closed surface in the complements of closed braid has relativ…