1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

LECTURE 3. THE WEINSTEIN CONJECTURE IN THE OVERTWISTED CASE 69

by the set
1

{(x, y, -2xy) I (x, y) E B 0 (0) C JR^2 }

with some E > 0 and e corresponds to the elliptic singular point (0, 0, 0). The

contact structure is given by

and we define a complex structure on ker A as follows: For (x, y, z) near (0, 0, 0) we
put

J(x,y,z) ( ~ ) - ( Jx )

Figure 7. Starting from an overtwisted disk and ending up with a better one

after applying the Giroux elimination process. Note however that the better

disk might have a different boundary than the disk we started with.

Figure 8. This schematic picture shows the Bishop family. The plane F

represents the disk V.