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${\bf Z}\sb 2$-fixed sets of stationary point free ${\bf Z}\sb 4$-actions

${\bf Z}\sb 2$-fixed sets of stationary point free ${\bf Z}\sb 4$-actions

In this work we consider the question: Which classes in the unoriented bordism group of free ${\mathbb {Z}_2}$-actions can be realized as the ${\mathbb {Z}_2}$-fixed set of stationary point free ${\mathbb {Z}_4}$-action on a closed manifold with ${\mathbb {Z}_2}$-fixed point set having constant codimension $k$?