Suppose φ : L ⊗ L →Z is the
equivariant intersection form of a highly-connected manifold admitting a Zp-action, p
an odd prime, so in particular L is an integral representation of Zp. We first derive
conditions on L. Then we show that if φ is any even unimodular form on an L
satisfying these conditions, there is a highly-connected manifold M admitting a
piecewise-linear Zp-action having a form Witt-equivalent to φ as its intersection
form. We also prove the analogous statement for torsion linking forms of
odd-dimensional manifolds. Finally, we consider the smoothing question for the
actions we construct.
