
Symmetry in Nonlinear Mathematical Physics  2009
Olga Kunakovskaya (Voronezh State University, Russia)
Alfonso Vignoli (Universita degli Studi di Roma "Tor Vergata", Italy)
Antonio Vitolo (Universita degli Studi di Salerno, Italy)
Equivariant vector fields and their indices
Abstract:
We introduce Γequivariant local and global (total) indices of connected components of the zero set of a smooth Γequivariant (co)tangent vector field on a compact ndimensional smooth manifold (possibly with boundary) with a given smooth action of a compact Lie group Γ. These indices belong to Γequivariant homotopy groups of spheres. The basis of our construction is the Ize–Vignoli degree theory of Γequivariant maps. Two existence theorems of solutions for nonlinear problems of Equivariant Analysis are obtained.

