On the support genus of Legendrian knots


ARCHIV DER MATHEMATIK, 2020 (SCI İndekslerine Giren Dergi) identifier identifier


In this paper, we show that any topological knot or link in S-1 x S-2 sits on a planar page of an open book decomposition whose monodromy is a product of positive Dehn twists. As a consequence, any knot or link type in S-1 x S-2 has a Legendrian representative having support genus zero. We also show this holds for some knots and links in the lens spaces L(p, 1).