Related papers: Singular chains on topological stacks
In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…
We show that the natural algebraic structure of the singular chains on a path connected topological space determines the fundamental group functorially. Moreover, we describe a notion of weak equivalence for the relevant algebraic structure…
We develop a theory of singular support for various infinite dimensional stacks and establish several functoriality properties. Then we apply this theory to compute the singular support of the Grothendieck-Springer affine Springer sheaf and…
We observe that the notion of a trivial Serre fibration, a Serre fibration, and being contractible, for finite CW complexes, can be defined in terms of the Quillen lifting property with respect to a single map M-->/\ of finite topological…
We study relative integral functors for singular schemes and characterise those which preserve boundness and those which have integral right adjoints. We prove that a relative integral functor is an equivalence if and only if its…
We study composed map germs with respect to their local fibrations. Under most general conditions, inspired by the tameness condition that was introduced recently, we prove the existence of singular tube fibrations, and we determine the…
In a recent paper we introduced a much weaker and easy to verify structure than a model category, which we called a "weak fibration category". We further showed that a small weak fibration category can be "completed" into a full model…
We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of…
We construct a model category structure on the category of diffeological spaces which is Quillen equivalent to the model structure on the category of topological spaces based on the notions of Serre fibrations and weak homotopy…
Classification questions are often about understanding components of a category. It is much more desirable however to be able to understand the entire homotopy type of this category and not just the set of its components. In this paper we…
Lannes' T-functor is used to give a construction of the Singer functor R_1 on the category U of unstable modules over the Steenrod algebra A. This leads to a direct proof that the composite functor Fix R_1 is naturally equivalent to the…
There are infinitely many variants of the notion of Kan fibration that, together with suitable choices of cofibrations and the usual notion of weak equivalence of simplicial sets, satisfy Quillen's axioms for a homotopy model category. The…
We show that the fibrant objects in the minimal model structure on the category of simplicial sets are characterized by a lifting condition with respect to maps which resemble the horn inclusions that define Kan complexes.
A Vec-variety is a suitable functor from finite-dimensional vector spaces to finite-dimensional varieties. Most varieties in the geometry of tensors, e.g. the variety of d-way tensors of slice rank at most r, are of this form. We prove that…
We show that the sequentially $(S_r)$ condition for simplicial complexes is a topological property. Along the way, we present an elementary proof for the fact that the Serre's condition $(S_r)$ is a topological property.
Let F be a fibration on a simply-connected base with symplectic fibre (M, \omega). Assume that the fibre is nilpotent and T^{2k}-separable for some integer k or a nilmanifold. Then our main theorem, Theorem 1.8, gives a necessary and…
Parallel transport in a fibre bundle with respect to smooth paths in the base space B have recently been extended to representations of the smooth singular simplicial set Sing_{smooth}(B). Inspired by these extensions,I revisit the…
We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is equivalent to the classification of simple semitoric systems…
A general construction is found for `topological' singular vectors of the twisted N=2 superconformal algebra. It demonstrates many parallels with the known construction for sl(2) singular vectors due to Malikov--Feigin--Fuchs, but is…
We develop a homotopical framework for small categories that extends classical invarints of algebraic topology to the categorical setting. Our approach is based on the construction of genuine path category, obtained trough a localization…