Related papers: Homotopy limits and fixed point stacks
We exploit the theory of $\infty$-stacks to provide some basic definitions and calculational tools regarding stratified homotopy theory of stratified topological stacks.
We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms. These homotopy types are viewed as systems (or functors),…
We describe the relation of $r$-similarity and finite-order invariants on the homotopy set $[S^1,Y]=\pi_1(Y)$.
This paper defines homology in homotopy type theory, in the process stable homotopy groups are also defined. Previous research in synthetic homotopy theory is relied on, in particular the definition of cohomology. This work lays the…
This paper contains two results on how homotopy limits of topological spaces interact with connectivity. The first is a formula for the connectivity of the homotopy limit of diagrams shaped over suitably finite categories, in terms of the…
Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the challenges posed by this approach to formalizing homotopy-theoretic…
We study the relation between the lattice points of a stacky polytope and a prequantisation of the stack associated to the stacky polytope. We introduce a prequantisation of a Deligne--Mumford stack and discuss the uniqueness and the…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
This note records that the Langlands parameter spaces, associated by Adams- Barbasch-Vogan to a real group, may be described as homotopy fixed points (fixed point stacks) of the spaces associated to the corresponding complex group.
We give a new description of Rosenthal's generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.
For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces…
The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
We survey various approaches to axiomatic stable homotopy theory, with examples including derived categories, categories of (possibly equivariant or localized) spectra, and stable categories of modular representations of finite groups. We…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
To various kinds of quadratic functors, homotopy types of two stage spaces are assigned. It is investigated what kind of homotopy types are obtainable in this way.
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
We use sheaf theory and the six operations to define and study the (equivariant) homology of stacks. The construction makes sense in the algebraic, complex-analytic, or even topological categories.