Related papers: Homotopy idempotent functors on classifying spaces

The moduli spaces refered to are topological spaces whose path components parametrize homotopy types. Such objects have been studied in two separate contexts: rational homotopy types, in the work of several authors in the late 1970's; and…

We calculate the ku-homology of the groups Z/p^n X Z/p and Z/p^2 X Z/p^2. We prove that for this kind of groups the ku-homology contains all the complex bordism information. We construct a set of generators of the annihilator of the…

We identify the obstructions for the functoriality and the uniqueness of the totalization functor, (partially) defined on the category of simplicial objects in the homotopy category of a stable model category, and we use a result from the…

Let p be a fibration of simply connected CW complexes with finite base B and fibre F. Let aut_1(p) denote the identity component of the space of all fibre-homotopy self-equivalences of p and Baut_1(p) the classifying space for this…

Given a functor $p:E \rightarrow B$ and an object $e \in E$ , we define a \emph{displacement} of $e$ along a morphism $\varepsilon: p(e) \rightarrow b$, as a map $e \rightarrow \nabla_\varepsilon(e)$ satisfying a universal property analogue…

Consider a Hamiltonian action of a compact Lie group H on a compact symplectic manifold (M,w) and let G be a subgroup of the diffeomorphism group Diff(M). We develop techniques to decide when the maps on rational homotopy and rational…

We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric…

Fix an odd prime $p$ and let $X$ be the $p$-localization of a finite suspended $CW$-complex. Given certain conditions on the reduced mod-$p$ homology $\bar H_*(X;\zmodp)$ of $X$, we use a decomposition of $\Omega\Sigma X$ due to the second…

We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature. More precisely, we…

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a…

We characterize simplicial localization functors among relative functors from relative categories to simplicial categories as any choice of homotopy inverse to the delocalization functor of Dwyer and the second author.

We extend the standard localization theory for function and section spaces due to Hilton-Mislin-Roitberg and Moller outside the CW category to the case of compact metric domain in the presence of a grouplike structure. We study applications…

We study the homological algebra in the category $\mathcal{P}_p$ of strict polynomial functors of degree $p$ over a field of positive characteristic $p$. We determine the decomposition matrix of our category and we calculate the Ext-groups…

A p-compact group is a mod p homotopy theoretical analogue of a compact Lie group. It is determined the homotopy nilpotency class of a p-compact group having the homotopy type of the $p$-completion of the direct product of spheres.

To every homotopy n-nilpotent group, defined in earlier work by Dwyer and the author, we associate an endofunctor of pointed spaces and prove that it is looped and n-excisive. As a tool we prove that $\Omega P_n({\rm id})$ commutes with…

We introduce and study the category of $p$-bifree biset functors for a fixed prime $p$, defined via bisets whose left and right stabilizers are $p'$-groups. This category naturally lies between the classical biset functors and the diagonal…

We relate stability properties (i.e. moment exponents) of a stochastic dynamical system on a compact manifold $M$ to the homotopy and integral homology groups of $M$. In the special case of gradient Brownian systems associated to isometric…

The inclusion hyperspace functor, the capacity functor and monads for these functors have been extended from the category of compact Hausdorff spaces to the category of Tychonoff spaces. Properties of spaces and maps of inclusion…

Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular,…

In this paper we complete the description of the $B\mathbb{Z} /p$-cellularization of the classifying spaces of all finite groups, for all primes $p$. The techniques are based in a careful analysis of the $p$-fusion structure of the groups…