Equivariant Nielsen fixed point theory for G-maps
Let f: \(V\to X\) be a G-map defined on an open invariant subset V of a G- ENR X where G is a compact Lie group and the G-action on V is not necessarily free. In this paper, we introduce the notion of an equivariant Nielsen number \(N^ c_ G(f,V)\) which is an ordered k-tuple that depends on the isotropy types \((H_ 1),...,(H_ k)\) of V. When G is finite, \(N^ c_ G(f,V)\) gives a lower bound for the minimal number of fixed points in the (restricted) G-homotopy class of f and this lower bound is sharp when the G-action of V is free. We relate \(N^ c_ G(f,V)\) to a local equivariant obstruction to G-deforming a map to be fixed point free and we discuss the relationship between the equivariant Nielsen number and the ordinary Nielsen number.
scientific article; zbMATH DE number 4131257