Equivariant rational homotopy theory as a closed model category
نویسندگان
چکیده
منابع مشابه
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...
متن کاملOn Equivariant Homotopy Theory for Model Categories
Two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category are studied and compared. For the topological model category of spaces, we recover that the categories of topological presheaves indexed by the orbit category of a fixed topological group G and the category of G-spaces form Quillen equivalent model categories.
متن کاملEquivariant Homotopy Theory
In this note we announce an obstruction theory for extending (continuous) equivariant maps defined on a certain class of G-spaces, where G is a compact Lie group. The details of this work will be published elsewhere. Our results barely touch upon the attendant problem of providing techniques that would serve in practice for the computation of the obstruction groups. In general this last problem...
متن کاملEquivariant stable homotopy theory
We will study equivariant homotopy theory for G a finite group (although this often easily generalizes to compact Lie groups). The general idea is that if we have two G-spaces X and Y , we’d like to study homotopy classes of equivariant maps between them: [X,Y ] = Map(X,Y )/htpy, where Map(X,Y ) = {f : X → Y |f(gx) = gf(x) for all g ∈ G}. In classical homotopy theory (i.e. when G is the trivial...
متن کاملA Survey of Equivariant Stable Homotopy Theory
EQUIVARIANT stable homotopy theory was invented by G. B. Segal in the early 1970s [45]. He was motivated by his work with Atiyah [9] on equivariant K-theory, generalizing an earlier theorem of Atiyah’s on the K-theory of classifying spaces of finite groups to compact Lie groups, and by his work on configuration space and discrete models for iterated loop spaces. His work also suggested to him t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1998
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00127-8