Involutions and stationary point free \(\mathbb{Z}_ 4\)-actions (Q1203589)

We study fixed-point sets of involutions and \(\mathbb{Z}_ 2\)-fixed-point sets of stationary-point-free \(\mathbb{Z}_ 4\)-actions. We determine which classes in the Thom's bordism ring can be realized as the fixed-point set of an involution on an \(n\)-dimensional manifold. Also, we determine which classes in the bordism group of free involutions can be realized as the \(\mathbb{Z}_ 2\)-fixed-point set of a stationary-point-free \(\mathbb{Z}_ 4\)- action.