  Let $S$ be a closed orientable spin manifold. Let $K \subset S$ be a
submanifold and denote its complement by $M_K$. In this paper we prove that
there exists an isomorphism between partially wrapped Floer cochains of a
cotangent fiber stopped by the unit conormal $\varLambda_K$ and chains of a
Morse theoretic model of the based loop space of $M_K$, which intertwines the
$A_\infty$-structure with the Pontryagin product. As an application, we
restrict to codimension 2 spheres $K \subset S^n$ where $n = 5$ or $n\geq 7$.
Then we show that there is a family of knots $K$ so that the partially wrapped
Floer cohomology of a cotangent fiber is related to the Alexander invariant of
$K$. A consequence of this relation is that the link $\varLambda_K \cup
\varLambda_x$ is not Legendrian isotopic to $\varLambda_{\mathrm{unknot}} \cup
\varLambda_x$ where $x\in M_K$.
