We study moduli spaces M of holomorphic maps U from Riemann
surfaces to R4 with boundaries on the Lagrangian cylinder over a
Legendrian link Ξβ(R3,ΞΎstdβ). We allow our
domains, Ξ£, to have non-trivial topology in which case M is
the zero locus of an obstruction function O, sending a moduli space
of holomorphic maps in C to H1(Ξ£).
In general, Oβ1(0) is not combinatorially computable. However
after a Legendrian isotopy, Ξ can be made left-right-simple, implying
that any U of index 1 is a disk with one or two positive punctures for
which ΟCββU is an embedding. Moreover, any U of index 2
is either a disk or an annulus with ΟCββU simply covered
and without interior critical points. Therefore any SFT invariant of Ξ
is combinatorially computable using only disks with β€2 positive
punctures.Comment: 42 pages. V3: Minor change