  The N=1,d=10 superYang-Mills action is constructed in a twisted form, using
SU(5)-invariant decomposition of spinors in 10 dimensions. The action and its
off-shell closed twisted scalar supersymmetry operator Q derive from a
Chern-Simons term. The action can be decomposed as the sum of a term in the
cohomology of Q and of a term that is Q-exact. The first term is a fermionic
Chern-Simons term for a twisted component of the Majorana-Weyl gluino and it is
related to the second one by a twisted vector supersymmetry with 5 parameters.
The cohomology of Q and some topological observables are defined from descent
equations. In this SU(5)<SO(10)$ invariant decomposition, the N=1, d=10 theory
is determined by only 6 supersymmetry generators, as in the twisted N=4, d=4
theory. There is a superspace with 6 twisted fermionic directions, with
solvable constraints.
