A stable approach to the equivariant Hopf theorem

Abstract

Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner [S. Waner, Equivariant RO(G)-graded bordism theories, Topology and its Applications 17 (1984) 1-26], the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterised in terms of congruences. This is first shown to be a stable problem, and then solved using methods of equivariant stable homotopy theory with respect to a semi-free G-universe.

Bauer-Furuta Invariants and Galois Symmetries

“…There is an equivariant stable Hopf theorem, see [23], which tells us that in this situation the ghost map is injective with a cokernel of order p, and that the elements in the image are characterised by a certain congruence. In our situation this reads as follows.…”

A non-trivial ghost kernel for the equivariant stable cohomotopy of projective spaces

“…see [8], where it is shown that the ghost map is injective in that case. As it will turn out, we can change this if we replace W by W /RG, and this is situation studied here.…”

A Non-trivial Ghost Kernel for Complex Projective Spaces with Symmetries

“…(see [Szy07a], where it is shown that the ghost map is injective in that case). As it will turn out, we can change this if we replace W by W/ RG, and this is the situation studied here.…”