  It is proved that fundamental groups of boolean representable simplicial
complexes are free and the rank is determined by the number and nature of the
connected components of their graph of flats for dimension $\geq 2$. In the
case of dimension 2, it is shown that boolean representable simplicial
complexes have the homotopy type of a wedge of spheres of dimensions 1 and 2.
Also in the case of dimension 2, necessary and sufficient conditions for
shellability and being sequentially Cohen-Macaulay are determined. Complexity
bounds are provided for all the algorithms involved.
