Some remarks on degree theory for ${\rm SO}(2)$-equivariant transversal maps

Abstract

The aim of this article is to introduce a new class ${\rm SO}(2)$-equivariant transversal maps $\mathcal{TR}({\rm cl}(\Omega),\partial \Omega)$ and to define degree theory for such maps. We define degree for ${\rm SO}(2)$-equivariant transversal maps and prove some properties of this invariant. Moreover, we characterize ${\rm SO}(2)$-equivariant transversal isomorphisms and derive formula for degree of such isomorphisms.