Equivariant vector fields and self-maps of spheres. (Q1420631)

This is a new tentative to generalize the Euler characteristic definition in the equivariant situation. The purpose here is to recover the property to be the unique obstruction to the existence of a nowhere zero smooth equivariant tangent vector field by a compact Lie group action. The authors introduce first pseudotransversality results for equivariant vector fields, then they define the strong equivariant Euler characteristic of a G-CW complex as the equivariant transfer associated to the fibration \(X \mapsto *\). As a corollary they give the calculus of the monoid of self-maps of a sphere.