The stable signature of a regular cyclic action (Q2750913)

The author studies nonfree regular \(G_p\)-actions on \(2n\)-dimensional oriented manifolds \(M^{2n}\), where \(p\) is an odd prime and \(G_p\) denotes the cyclic group of order \(p\). Let \(g\) be a generator of \(G_p\). The main result of the paper is that if the \(g\)-signature \(\text{Sign} (g,M)\) is a rational integer and \(n<p-1\), then there exists a choice of orientations such that the \(g\)-signature of the action equals the signature of the fixed point set. The author also gives some relations between the \(g\)-signature of the action and the dimensions of the components of the fixed point set.