Related papers: Compact groups and absolute extensors

We study the closures of subgroups, semilattices and different kinds of semigroup extensions in semitopological inverse semigroups with continuous inversion. In particularly we show that a topological group $G$ is $H$-closed in the class of…

A new highly symmetrical model of the compact Lie algebra $\mathfrak{g}^c_2$ is provided as a twisted ring group for the group $\mathbb{Z}_2^3$ and the ring $\mathbb{R}\oplus\mathbb{R}$. The model is self-contained and can be used without…

We construct examples of two-step and three-step nilpotent Lie groups whose automorphism groups are `small' in the sense of either not having a dense orbit for the action on the Lie group, or being nilpotent (the latter being stronger).…

In this paper we take a look at compactly generated weak Hausdorff spaces equipped with an action of a compact Lie group $G$ together with their colimits and homotopy colimits. In particular, we investigate relations between (homotopy)…

We study extensively the homotopy theory of coalgebras. By coalgebras, we mean the full theory of coalgebras: with counits and not necessarily locally conilpotent. For example $\mathcal E_\infty$-coalgebras, $\mathcal A_\infty$-coalgebras,…

Given a Lie group $G$ with finitely many components and a compact Lie group A which acts on $G$ by automorphisms, we prove that there always exists an A-invariant maximal compact subgroup K of G, and that for every such K, the natural map…

We analyse the homotopy types of gauge groups of principal U(n)-bundles associated to pseudo Real vector bundles in the sense of Atiyah. We provide satisfactory homotopy decompositions of these gauge groups into factors in which the…

For each positive integer Q there exists a path connected metric compactum X such that the Qth-homotopy group of X is compactly generated but not a topological group (with the quotient topology).

We give a classification, up to local isomorphisms, of semi-simple Lie groups without compact factors that can act faithfully and conformally on a compact Lorentz manifold of dimension greater than or equal to $3$.

The compact, connected Lie group $E_6$ admits two forms: simply connected and adjoint type. As we previously established, the Baum-Connes isomorphism relates the two Langlands dual forms, giving a duality between the equivariant K-theory of…

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…

We develop a homotopy theory for additive categories endowed with endofunctors, analogous to the concept of a model structure. We use it to construct the homotopy theory of a Hovey triple (which consists of two compatible complete cotorsion…

Lie groups considered as three-dimensional almost paracontact almost paracomplex Riemannian manifolds are investigated. In each basic class of the classification used for the manifolds under consideration, a correspondence is established…

We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to…

We study Lie foliations on compact manifolds, in case the Lie group is compact. Our main results improve Tischler classical result on the existence of fibration and, as an application, we study the case the manifold has an amenable…

The main goal of this article is to develop integration theory for absolute partition $L_\infty$-algebras, which are point-set models for the (spectral) partition Lie algebras of Brantner-Mathew where infinite sums of operations are…

The bootstrap category in E-theory for C*-algebras over a finite space X is embedded into the homotopy category of certain diagrams of K-module spectra. Therefore it has infinite n-order for every n. The same holds for the bootstrap…

Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural…

In this note it is proved that the class of paratopologies is simple and that under the assumption that the measurable cardinals form a proper class, the class of hypotopologies is not simple. Moreover, an example is given of a Hausdorff…

We observe a correspondence between collections of closed subgroups and normal subgroups in totally disconnected locally compact groups. This correspondence is applied to prove structure theorems for two classes of totally disconnected…