  Let $M^n$ be a closed, connected $n$-manifold. Let $\mtm$ denote the Thom
spectrum of its stable normal bundle. A well known theorem of Atiyah states
that $\mtm$ is homotopy equivalent to the Spanier-Whitehead dual of $M$ with a
disjoint basepoint, $M_+$. This dual can be viewed as the function spectrum,
$F(M, S)$, where $S$ is the sphere spectrum. $F(M, S)$ has the structure of a
commutative, symmetric ring spectrum in the sense of \cite{hss}, \cite{ship}.
In this paper we prove that $\mtm$ also has a natural, geometrically defined,
structure of a commutative, symmetric ring spectrum, in such a way that the
classical duality maps of Alexander, Spanier-Whitehead, and Atiyah define an
equivalence of symmetric ring spectra, $\alpha : \mtm \to F(M, S)$. We discuss
applications of this to Hochshield cohomology representations of the
Chas-Sullivan loop product in the homology of the free loop space of $M$.
