  A fundamental ingredient in the noncommutative geometry program is the notion
of KK-duality, often called K-theoretic Poincar\'{e} duality, that generalises
Spanier-Whitehead duality. In this paper we construct a $\theta$-summable
Fredholm module that represents the fundamental class in KK-duality between the
stable and unstable Ruelle algebras of a Smale space. To find such a
representative, we construct dynamical partitions of unity on the Smale space
with highly controlled Lipschitz constants. This requires a generalisation of
Bowen's Markov partitions. Along with an aperiodic point-sampling technique we
produce a noncommutative analogue of Whitney's embedding theorem, leading to
the Fredholm module.
