Abstract: Let be a compact G-ENR
pair and a G-compactly
fixed map of pairs. We introduce the Nielsen-type number and show that it is invariant under
relative G-compactly fixed homotopies
and is a lower bound for the number of fixed points in the (restricted) relative
equivariant homotopy class of f. We also investigate when this invariant is an optimal such lower
bound, and provide examples that illustrate why it is a useful addition to the
collection of Nielsen-type numbers already in existence.
Keywords and phrases: equivariant fixed point theory, Nielsen fixed point theory, G-map.