Related papers: Straightening Banach-Lie-group-valued almost-cocyc…

We show that algebraic equivalence of images of stable maps of curves lifts to deformation equivalence of the stable maps. The main applications concern $A_1(X)$, the group of 1-cycles modulo algebraic equivalence, for smooth, separably…

In this paper, we investigate homological properties of Banach algebras. We show that retractions Banach algebras preserve biprojectivity, contractibility and biflatness. We also prove that contractibility of second dual of a Banach algebra…

In this article it is proved, that every locally compact second countable group has a left invariant metric d, which generates the topology on G, and which is proper, ie. every closed d-bounded set in G is compact. Moreover, we obtain the…

We prove that if a countable group $\Gamma$ contains infinite commuting subgroups $H, H'\subset \Gamma$ with $H$ non-amenable and $H'$ ``weakly normal'' in $\Gamma$, then any measure preserving $\Gamma$-action on a probability space which…

It is shown that every nonsingular continuous representation of the group algebra $L^{1}(G)$ in Banach spaces is completely reducible if and only if $G$ is a compact group.

Every lattice H in a connected semi-simple Lie group G acts properly discontinuously by isometries on the contractible manifold G/K (K a maximal compact subgroup of G). We prove that if H acts on a contractible manifold W and if either 1)…

We provide a new construction of a topological group model for the string group of a compact, simple, and simply-connected Lie group, by solving the obstruction realization problem for compact group $G$-kernels on full factors. Furthermore,…

Given a simple Lie group G of rank 1, we consider compact pseudo-Riemannian manifolds (M,g) of signature (p,q) on which G can act conformally. Precisely, we determine the smallest possible value for the index min(p,q) of the metric. When…

Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\mu)$ such that the Banach space…

We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is…

On a foliated manifold equipped with an action of a compact Lie group $G$, we study a class of almost-coupling Poisson and Dirac structures, in the context of deformation theory and the method of averaging.

We prove that actions of complex reductive Lie groups on a complex compact manifold are locally extendable to its Kuranishi family. This can be seen as an analogue of Rim's result (see [11]) in the analytic setting.

We prove that for every compactum $X$ and every integer $n \geq 2$ there are a compactum $Z$ of $\dim \leq n+1$ and a surjective $UV^{n-1}$-map $r: Z \lo X$ such that for every abelian group $G$ and every integer $k \geq 2$ such that…

We prove the $L_p$ Poincar\'e inequalities with constant $C\sqrt{p}$ for $1$-cocycles on countable discrete groups under Bakry--Emery's $\Gamma_2$-criterion. These inequalities determine an analogue of subgaussian behavior for 1-cocycles.…

Let $G$ be a compact group. For $1\leq p\leq\infty$ we introduce a class of Banach function algebras $\mathrm{A}^p(G)$ on $G$ which are the Fourier algebras in the case $p=1$, and for $p=2$ are certain algebras discovered in…

We show that for any cohomogeneity one continuous action of a compact connected Lie group $G$ on a closed topological manifold the equivariant cohomology equipped with its canonical $H^*(BG)$-module structure is Cohen-Macaulay. The proof…

In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of epsilon-quasi tiling techniques, we set…

Let $(G,\theta)$ be a Banach--Lie group with involutive automorphism $\theta$, $\g = \fh \oplus \fq$ be the $\theta$-eigenspaces in the Lie algebra $\g$ of $G$, and $H = (G^\theta)_0$ be the identity component of its group of fixed points.…

Assume that we are given a coaction \delta of a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle \omega on G. Motivated by the approach of Kasprzak to Rieffel's deformation we define a deformation A_\omega of A.…

The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present a condition implying that every affine isometric action of a given group $G$ on a reflexive…