Vol. 73, No. 1, 1977

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Topological realization of equivariant intersection forms

Steven Howard Weintraub

Vol. 73 (1977), No. 1, 257–280

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.

Mathematical Subject Classification
Primary: 57E99, 57E99
Received: 15 March 1976
Revised: 19 November 1976
Published: 1 November 1977
Steven Howard Weintraub