On the support genus of Legendrian knots


ONARAN S.

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

Özet

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).