Isovariant extensors and the characterization of equivariant homotopy equivalences

Isovariant mappings of degree 1 and the Gap Hypothesis

Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant— often coincide under a condition called the Gap Hypothesis; the proofs use deep results in geometric topology. This paper analyzes the difference between the two types of maps from a homotopy theoretic viewpoint more generally for degre...

Functoriality of Isovariant Homotopy Classification

It is a deep fact that the homotopy classification of topological manifolds is convariantly functorial. In other words, a map M → N of topological manifolds naturally induces a map S(M) → S(N) of their structure sets. We extend the fact to the isovariant structure set SG(M, rel Ms) of G-equivariant topological manifolds isovariantly homotopy equivalent to M and restricts to homormorphism on the...

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.

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

An Algebraic Model for Rational S-equivariant Stable Homotopy Theory

Greenlees defined an abelian category A whose derived category is equivalent to the rational S1-equivariant stable homotopy category whose objects represent rational S1equivariant cohomology theories. We show that in fact the model category of differential graded objects in A models the whole rational S1-equivariant stable homotopy theory. That is, we show that there is a Quillen equivalence be...