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The study of assignments was systematically first done in [1].
They introduced the notion of assignments and showed the ring of
assignments for any manifold M, A(M) is the zeroth space in a certain
sequence of vector spaces which they called assignment cohomology. In [2]
their idea was extended to introduce the notion of polynomial assignments.
We studied assignment cohomology for a class of manifolds called
Bott-Samelson manifolds(Z) introduced in [3]. We provide an inductive
construction of the assignment classes for Z and gave a basis for the
assignment ring, A(Z) in terms of these classes. It turned out that when Z
is GKM this gives a basis for the equivariant cohomology ring of Z,
H_T^*(Z)
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