Work of S. Akbulut and H. C. King show that every PL-manifold M is combinatorially equivalent to a real algebraic set A (possibly with singularities).
S. Akbulut and H. C. King. Real Algebraic Structures on Topological Spaces, Publ. I.H.E.S., Vol. 53 (1981), 79-162, MR #83h:58009
In their work, Akbulut and King do not show (as far as i remember) the explicit algebraic equations defining the algebraic set A.
My questions are: Does anyone know this work and how one could deduce the algebraic equations defining A ?? Also, and the most important of my two questions: Can these equations be defined with polynomials which have *only* rational coefficients ??