The Unstable Equivariant Fixed Point Index and the Equivariant Degree

A correspondence between the equivariant degree introduced byIze, Massabó, and Vignoli and an unstable version ofthe equivariant fixed point index defined by Prieto and Ulrichis shown. With the help of conormal maps and properties of theunstable index, a sum decomposition formula is proved for theindex and consequently also for the degree. As an application,equivariant homotopy groups are decomposed as direct sums ofsmaller groups of fixed orbit types, and a geometric interpretationof each summand is given in terms of conormal maps.