Related papers: Commutative classifying space for simplicial group…

We utilise the theory of crossed simplicial groups to introduce a collection of local Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site. As an application,…

In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…

Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group and the orthogonal group as well as Wang's quantum…

A connected homogeneous space X=G/K is called commutative if G is a connected Lie group, $K$ is a compact subgroup and the B*-algebra L^1(X)^K of K-invariant integrable function on X is commutative. In this article we introduce the space…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modelled by vector bundles over Brillouin tori,…

In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application…

This is a survey article with the goal to advertise spectrum valued versions of $K$- and $KK$- theory for $C^{*}$-algebras via a (stable and symmetric monoidal) $\infty$-categorical enhancement of Kasparov's classical $KK$-theory. The main…

In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth…

Let G be a discrete group for which the classifying space for proper G-actions is finite-dimensional. We find a space W such that for any such G, the classifying space PBG for proper G-bundles has the homotopy type of the W-nullification of…

Pseudotopological spaces are the Cartesian closed hull of the category of \v{C}ech closure spaces. In this paper, we give a direct proof that the model category of the pseudotopological spaces constructed by Rieser is Quillen equivalent to…

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…

Given a group action on a simplicial complex such that each simplex stabiliser admits a cocompact model of classifying space for proper actions, we give conditions implying the existence of a cocompact model of classifying space for proper…

A classification is given of the exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is determined as Lie…

We develop theory of multiplicity maps for compact quantum groups, as an application, we obtain a complete classification of right coideal $C^*$-algebras of $C(SU_q(2))$ for $q\in [-1,1]\setminus \{0\}$. They are labeled with Dynkin…

There is a well-known correspondence between the symplectic variety of representations of the fundamental group of a punctured Riemann surface into a compact Lie group G, with fixed conjugacy classes at the punctures, and a complex variety…

We consider a Hamiltonian action of a compact Lie group $G$ on a complete \ka manifold $M$ with a proper moment map. In a previous paper, we defined a regularized version of the Dolbeault cohomology of a $G$-equivariant holomorphic vector…

We consider the space of $n$-tuples of pairwise commuting elements in the Lie algebra of $U(m)$. We relate its one-point compactification to the subquotients of certain rank filtrations of connective complex $K$-theory. We also describe the…

We extend the formalism of Topological T-duality to spaces which are the total space of a principal $S^1$-bundle $p:E \to W$ with an $H$-flux in $H^3(E,Z)$ together the together with an automorphism of the continuous-trace algebra on $E$…

For a complete and cocomplete category $\mathcal{C}$ with a well-behaved class of `projectives' $\bar{\mathcal{P}}$, we construct a model structure on the category $s\mathcal{C}$ of simplicial objects in $\mathcal{C}$ where the weak…