Legendre whitehead linkleri

In this thesis we classify Legendrian positive Whitehead links in S^3 with the standard tight contact structure, (S^3,ξ_std), up to Legendrian isotopy. By using the convex surface theory on contact 3-manifolds we show how one can destabilize Legendrian positive Whitehead links in (S^3,ξ_std) until each component of it has Thurston-Bennequin number is -1. We also show that there are two Legendrian representatives of the positive Whitehead link with maximal Thurston-Bennequin number, tb=-2 and the same rotation number, r=0 . In addition to these, we show that the components can be interchanged by a Legendrian isotopy and the two different representatives of the positive Whitehead link with maximal Thurston-Bennequin number become the same after one single (positive or negative) stabilization. These results exhibit that Legendrian positive Whitehead links in (S^3,ξ_std) are not Legendrian simple.