For an arbitrary simplicial complex
,
Davis and Januszkiewicz have defined a family of homotopy equivalent CW–complexes
whose integral cohomology rings are isomorphic to the Stanley–Reisner algebra of
.
Subsequently, Buchstaber and Panov gave an alternative construction (here called
),
which they showed to be homotopy equivalent to Davis and Januszkiewicz’s
examples. It is therefore natural to investigate the extent to which the homotopy
type of a space is determined by having such a cohomology ring. We begin
this study here, in the context of model category theory. In particular, we
extend work of Franz by showing that the singular cochain algebra of
is formal as a differential graded noncommutative algebra. We specialise
to the rationals by proving the corresponding result for Sullivan’s
commutative cochain algebra, and deduce that the rationalisation of
is unique for a special
family of complexes
.
In a sequel, we will consider the uniqueness of
at
each prime separately, and apply Sullivan’s arithmetic square to produce
