  In this paper, we will be concerned with the explicit classification of
closed, oriented, simply-connected spin manifolds in dimension eight with
vanishing cohomology in the odd dimensions. The study of such manifolds was
begun by Stefan M\"uller. In order to understand the structure of these
manifolds, we will analyze their minimal handle presentations and describe
explicitly to what extent these handle presentations are determined by the
cohomology ring and the characteristic classes. It turns out that the
cohomology ring and the characteristic classes do not suffice to reconstruct a
manifold of the above type completely. In fact, the group ${\rm
Aut_0}\bigl(#_{i=1}^b(S^2\times S^5)\bigr)/{\rm Aut}_0\bigl(#_{i=1}^b
(S^2\times D^6)\bigr)$ of automorphisms of $#_{i=1}^b(S^2\times S^5)$ which
induce the identity on cohomology modulo those which extend to
$#_{i=1}^b(S^2\times D^6)$ acts on the set of oriented homeomorphy classes of
manifolds with fixed cohomology ring and characteristic classes, and we will be
also concerned with describing this group and some facts about the above
action.
