Minimal Models for Non-Free Circle Actions

Let $\Phi \colon \sbat \times M \to M$ be a smooth action of the unit circle $\sbat$ on a manifold $M$. In this work, we compute the minimal model of $M$ in terms of the orbit space $B$ and the fixed point set $F\subset B$, as a dg-module over the Sullivan's minimal model of $B$.