A Hopf type theorem for equivariant local maps

Abstract

We study otopy classes of equivariant local maps and prove the Hopf type theorem for such maps in the case of a real finite dimensional orthogonal representation of a compact Lie group.

Product Property of Equivariant Degree Under the Action of a Compact Abelian Lie Group

“…Observe that p i : E i → M i is a vector bundle such that rank E i = dim M i and E i is orientable as a manifold. Following tom Dieck (1979) and Bartłomiejczyk (2017), we define a function θ i :…”

Degree product formula in the case of a finite group action

“…In papers [1,2,6] the authors introduce the equivariant degree deg G : C G (V) → A(G) for the action of a compact Lie group G and prove that the degree has the following expected properties.…”

“…In the above we used two properties of the classical topological degree: the product formula (1) and the localization of zeros (2).…”

On the space of equivariant local maps

“…Remark 6.4. A more thorough description of F G [Ω] based on the formula (6.1) and the detailed analysis of the factors F W H [Ω H ] is given in [3], which continues and develops the approach presented here.…”