  Let $\mathcal{H}$ be a hypergraph on a finite set $V$. A {\em cover} of
$\mathcal{H}$ is a set of vertices that meets all edges of $\mathcal{H}$. If
$W$ is not a cover of $\mathcal{H}$, then $W$ is said to be a {\em noncover} of
$\mathcal{H}$. The {\em noncover complex} of $\mathcal{H}$ is the abstract
simplicial complex whose faces are the noncovers of $\mathcal{H}$. In this
paper, we study homological properties of noncover complexes of hypergraphs. In
particular, we obtain an upper bound on their Leray numbers. The bound is in
terms of hypergraph domination numbers. Also, our proof idea is applied to
compute the homotopy type of the noncover complexes of certain uniform
hypergraphs, called {\em tight paths} and {\em tight cycles}. This extends to
hypergraphs known results on graphs.
