Connect sum and transversely non simple knots

We prove that transversal non-simplicity is preserved under taking connect sum, generalizing Vertesi's result.Comment: Following the referee, exposition is changed and misprints are correcte

Overtwisted discs in planar open books

Using open book foliations we show that an overtwisted disc in a planar open book can be put in a topologically nice position. As a corollary, we prove that a planar open book whose fractional Dehn twist coefficients grater than one for all the boundary components supports a tight contact structure.Comment: 32 pages, 26 figures. Accepted by International Journal of Mathematic