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math.GT2009★ 3 cited
Homologically thin, non-quasi-alternating links
Joshua Greene
We exhibit the first examples of links which are homologically thin but not quasi-alternating. To show that they are not quasi-alternating, we argue that none of their branched dou…
math.GT2009★ 10 cited
On closed 3-braids with unknotting number one
Joshua Greene
We prove that if an alternating 3-braid knot has unknotting number one, then there must exist an unknotting crossing in any alternating diagram of it, and we enumerate such knots.…