  Let $\gS=(V,E)$ be a finite, $d$-regular bipartite graph. For any $\lambda>0$
let $\pi_\lambda$ be the probability measure on the independent sets of $\gS$
in which the set $I$ is chosen with probability proportional to $\lambda^{|I|}$
($\pi_\lambda$ is the {\em hard-core measure with activity $\lambda$ on
$\gS$}). We study the Glauber dynamics, or single-site update Markov chain,
whose stationary distribution is $\pi_\lambda$. We show that when $\lambda$ is
large enough (as a function of $d$ and the expansion of subsets of
single-parity of $V$) then the convergence to stationarity is exponentially
slow in $|V(\gS)|$. In particular, if $\gS$ is the $d$-dimensional hypercube
$\{0,1\}^d$ we show that for values of $\lambda$ tending to 0 as $d$ grows, the
convergence to stationarity is exponentially slow in the volume of the cube.
The proof combines a conductance argument with combinatorial enumeration
methods.
