相关论文: The chromatic filtration of the Burnside category

Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.

We introduce \emph{flagged $(\infty,n)$-categories} and prove that they are equivalent to Segal sheaves on Joyal's category ${\mathbf\Theta}_n$. As such, flagged $(\infty,n)$-categories provide a model-independent formulation of Segal…

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant…

We study the uniqueness of enhancements of tensor-triangulated categories. To do so, we provide conditions under which these enhancements interact well with categorical decompositions. As an application we obtain new results about the…

We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.

For a finite p-group G and a bounded below G-spectrum X of finite type mod p, the G-equivariant Segal conjecture for X asserts that the canonical map X^G --> X^{hG} is a p-adic equivalence. Let C_{p^n} be the cyclic group of order p^n. We…

We discuss filtrations arising from de Rham-type cohomology theories for $E_\infty$ rings and $E_n$ rings. Examples include the HKR filtration on relative topological Hochschild homology, the Hodge filtration on $E_\infty$ infinitesimal…

Over a monoidal model category, under some mild assumptions, we equip the categories of colored PROPs and their algebras with projective model category structures. A Boardman-Vogt style homotopy invariance result about algebras over…

Suppose F is a special Gamma-space equipped with a natural transformation to the infinite symmetric power functor. Segal's infinite loop space machine associates with F a spectrum, denoted kF, equipped with a map to the integral…

In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fixed poset $P$, and show that it is a simplicial…

This paper is concerned with two conjectures which are intimately related. The first is a generalization to hypergraphs of Vizing's Theorem on the chromatic index of a graph and the second is the well-known conjecture of Erd\H{o}s, Faber…

The assignment of classifying spectra to saturated fusion systems was suggested by Linckelmann and Webb and has been carried out by Broto, Levi and Oliver. A more rigid (but equivalent) construction of the classifying spectra is given in…

We study the limit of the chromatic tower for not necessarily finite spectra, obtaining a generalization of the chromatic convergence theorem of Hopkins and Ravenel. Moreover, we prove that in general this limit does not coincide with…

Inside a symplectic leaf of the cluster Poisson variety of Borel-decorated $PGL_2$ local systems on a punctured surface is an isotropic subvariety we will call the chromatic Lagrangian. Local charts for the quantized cluster variety are…

We develop a theory of enriched categories over a (higher) category M equipped with a class W of morphisms called homotopy equivalences. We call them Segal M_W -categories. Our motivation was to generalize the notion of "up-to-homotopy…

We consider Rumin's filtration on the de Rham complex of a Carnot group. Although Pansu pullback by a Sobolev map is filtration preserving, it need not be a chain mapping. Nonetheless, we show that Pansu pullback induces a mapping of the…

We define a category of filtered topological spaces and explore some of its homotopy theoretic properties, including a filtered analogue of CW approximation. With this, we define and study a filtered (weighted) variant of the Euler…

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural…

We formulate and prove a version of the Segal Conjecture for infinite groups. For finite groups it reduces to the original version. The condition that G is finite is replaced in our setting by the assumption that there exists a finite model…

We prove that homotopy invariants of finite degree distinguish homotopy classes of maps of a connected compact CW-complex to a nilpotent connected CW-complex with finitely generated homotopy groups.