On the equivariant Hopf theorem

Isovariant Borsuk-Ulam results for pseudofree circle actions and their converse

“…For that purpose we shall introduce the multidegree and show a variant of the equivariant Hopf theorem. (See [5,II 4], [9] for the equivariant Hopf theorem.) Throughout this section, M is an orientable, connected, closed S 1 -manifold of type PF and we assume that Iso(M ) ⊂ Iso(SW ).…”

Degree of T-equivariant maps in Rn

“…It is shown that if there is a T -equivariant homotopy joining f to g then there is a T -equivariant gradient homotopy joining f to g. Our result suggests that there is no interesting generalization of T -equivariant degree on gradient vector fields. The proof is based on the latest results by Ferrario (see [4]) and Dancer, Gęba and Rybicki (see [1]). …”

A stable approach to the equivariant Hopf theorem

“…See Section 8.4. in [4], [10], Section II.4 in [5], or [3], [2], [7], and the references therein for recent contributions. All of these work unstably with a fairly elaborate obstruction machinery.…”