Related papers: Homotopy Theory of Orbispaces

We present a slight variation on a notion of weak \infty-groupoid introduced by Grothendieck in Pursuing Stacks and we study the homotopy theory of these \infty-groupoids. We prove that the obvious definition for homotopy groups of…

We construct an $(\infty,1)$-functor that takes each smooth $G$-manifold with corners $M$ to the space of equivariant smooth $h$-cobordisms ${\mathcal H}_{\mathrm{Diff}}(M)$. We also give a stable analogue ${\mathcal H}^{\mathcal…

Inspired by Segal-Stolz-Teichner project for geometric construction of elliptic (tmf) cohomology, and ideas of Floer theory and of Hopkins-Lurie on extended TFT's, we geometrically construct some $Ring$-valued representable cofunctors on…

Algebraic topological methods have been used successfully in concurrency theory, the domain of theoretical computer science that deals with distributed computing. L. Fajstrup, E. Goubault, and M. Raussen have introduced partially ordered…

Let $\mc G$ be a reductive group over an algebraically closed field of characteristic $p>0$. We study homogeneous $\mc G$-spaces that are induced from the $G\times G$-space $G$, $G$ a suitable reductive group, along a parabolic subgroup of…

Given an appropriate diagram of left Quillen functors between model categories, one can define a notion of homotopy fiber product, but one might ask if it is really the correct one. Here, we show that this homotopy pullback is well-behaved…

Given a higher-rank graph $\Lambda$, we investigate the relationship between the cohomology of $\Lambda$ and the cohomology of the associated groupoid $G_\Lambda$. We define an exact functor between the abelian category of right modules…

For a space X acted by a finite group $\G$, the product space $X^n$ affords a natural action of the wreath product $\Gn$. In this paper we study the K-groups $K_{\tG_n}(X^n)$ of $\Gn$-equivariant Clifford supermodules on $X^n$. We show that…

Given a general finite group $G$, there are various finite categories whose cohomology theories are of great interests. Recently Balmer and Grodal gave some new characterizations of the groups of endotrivial modules, via \v{C}ech cohomology…

Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…

This paper studies the foundations of the geometric fixed point functor in multiplicative equivariant stable homotopy theory. We introduce a new class of equivariant orthogonal spectra called generalized orbit desuspension spectra and…

We prove that the homotopy theory of cofibration categories is equivalent to the homotopy theory of cocomplete quasicategories. This is achieved by presenting both homotopy theories as fibration categories and constructing an explicit…

In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…

Let U be a unipotent group over the field of complex numbers C, acting on a complex algebraic variety X. Assume that there exists a surjective morphism of complex algebraic varieties f: X --> Y whose fibres are orbits of U. We show that if…

We give a homotopy theoretic characterization of stacks on a site $\cC$ as the {\it homotopy sheaves} of groupoids on $\cC$. We use this characterization to construct a model category in which stacks are the fibrant objects. We compare…

Suppose $G$ is a finite group acting on an Abelian variety $A$ such that the coarse moduli space $A/G$ is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal…

First we study the Gorenstein cohomological dimension ${\rm Gcd}_RG$ of groups $G$ over coefficient rings $R$, under changes of groups and rings; a characterization for finiteness of ${\rm Gcd}_RG$ is given. Some results in literature…

We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced functor between categories of algebras is an equivalence…

We construct a category of fibrant objects $\mathbb{C}\langle P\rangle$ in the sense of K. Brown from any indexed frame (a kind of indexed poset generalizing triposes) $P$, and show that its homotopy category is the Barr-exact category…

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…