Equivariant maps which are self homotopy equivalences

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

Reducibility of Self-homotopy Equivalences

We describe a new general method for the computation of the group Aut(X) of self-homotopy equivalences of a space. It is based on the decomposition of Aut(X) induced by a factorization of X into a product of simpler spaces. Normally, such decompositions require assumptions (’induced equivalence property’, ’diagonalizability’), which are strongly restrictive and hard to check. In this paper we d...

Isovariant extensors and the characterization of equivariant homotopy equivalences

We extend the well-known theorem of James–Segal to the case of an arbitrary family F of conjugacy classes of closed subgroups of a compact Lie group G: a G-map f : X → Y of metric Equiv F -ANE-spaces is a G-homotopy equivalence if and only if it is a weak G-F-homotopy equivalence. The proof is based on the theory of isovariant extensors, which is developed in this paper and enables us to endow ...

Spaces of Equivariant Self-equivalences of Spheres

Let F(ST) denote the identity component of the space of homotopy self-equivalences of STM and let F = inj limw FiS" ). This paper studies the homotopy properties of certain equivariant analogs of the infinite loop space F.

Self-Homotopy Equivalences of Product Spaces