  Let $\Sigma$ be a simply connected rational homology sphere. A pair of
disjoint closed submanifolds $M_+, M_-$ in $\Sigma$ are called dual to each
other if the complement $\Sigma - M_+$ strongly homotopy retracts onto $M_-$ or
vice-versa. In this paper we will give a complete answer of which integral
triples $(n; m_+, m_-)$ can appear, where $n=dim \Sigma -1$, $m_+={codim}M_+
-1$ and $m_-={codim}M_- -1$.
