  Based on the localization result for descendants in rational SFT moduli
spaces from our last joint paper, we prove topological recursion relations for
the Hamiltonian in SFT of symplectic mapping tori and in local SFT. Combined
with the dilaton equation in SFT, we use them to prove a reconstruction theorem
for descendants from primaries. While it turns out that (in contrast to
Gromov-Witten theory and non-equivariant cylindrical contact homology) the
descendant Hamiltonian cannot be computed from the Hamiltonian without
descendants alone, we get that the only additional piece of information needed
is the first descendant Hamiltonian, which counts holomorphic curves tangent to
the symplectic fibre. As already known from the explicit computations in local
SFT, it follows that the descendant SFT invariants in general contain more
geometric information than the primary SFT invariants.
