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The (co)homological dimension of homomorphism $\phi:G\to H$ is the maximal number $k$ such that the induced homomorphism is nonzero for some $H$-module. The following theorems are proven: THEOREM 1. For every homomorphism $\phi:G\to H$ of a…

Let \zeta be an n-dimensional complex matrix bundle over a compact metric space X and let A_\zeta denote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UA_\zeta, the group of unitaries of…

Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…

A \emph{complete geometric graph} consists of a set $P$ of $n$ points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bose, Hurtado, Rivera-Campo, and Wood, whether there exists a…

The aim of this paper is to show that the automorphism and isometry groups of the suspension of $B(H)$, $H$ being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism,…

Let $M$ be a compact connected orientable Seifert manifold with hyperbolic orbifold $B_M$, and $f_{\pi}: \pi_1(M)\rightarrow\pi_1(M)$ be an automorphism induced by an orientation-reversing homeomorphism $f$ of $M$. We give a bound on the…

We consider convergence sets of formal power series of the form $f(z,t)=\sum_{n=0}^{\infty} f_n(z)t^n$, where $f_n(z)$ are holomorphic functions on a domain $\Omega$ in $\mathbb{C}$. A subset $E$ of $\Omega$ is said to be a convergence set…

Let X=G/H be the quotient of a connected reductive algebraic C-group G defined over the field of complex numbers C by a finite subgroup H. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when H…

Perez-Marco proved the existence of non-trivial totally invariant connected compacts called hedgehogs near the fixed point of a nonlinearizable germ of holomorphic diffeomorphism. We show that if two nonlinearisable holomorphic germs with a…

We prove that a closed convex subset $C$ of a real Hilbert space $X$ has the fixed point property for $(c)$-mappings if and only if $C$ is bounded. Some convergence results about the iterations are obtained.

We study the subvariety of fixed points of an automorphism of a Calogero-Moser space induced by a regular element of finite order of the normalizer of the associated complex reflection group $W$. We determine some of (and conjecturally all)…

For any (Hausdorff) compact group $G$ with the normalized Haar measure ${\mathbf m}_G$, denote by ${\rm cp}(G)$ the probability ${\mathbf m}_{G\times G}(\{(x,y)\in G\times G \;|\; xy=yx\})$ of commuting a randomly chosen pair of elements of…

A right-invariant metric $\rho_{\alpha}$ on the compactly supported identity component $Cont_0(M,\alpha)$ of the group of contactomorphisms of an arbitrary contact manifold $(M,\alpha)$ is introduced in a similar way that the Hofer metric…

In this paper, we determine the homotopy type of the Morse complex of certain collections of simplicial complexes by studying dominating vertices or strong collapses. We show that if $K$ contains two leaves that share a common vertex, then…

A finite hypergraph $H$ consists of a finite set of vertices $V(H)$ and a collection of subsets $E(H) \subseteq 2^{V(H)}$ which we consider as partition of unity relations between projection operators. These partition of unity relations…

This paper deals with classifying the dynamics of {\it Topologically Anosov} plane homeomorphisms. We prove that a Topologically Anosov homeomorphism $f:\mathbb{R}^2 \to \mathbb{R}^2$ is conjugate to a homothety if it is the time one map of…

This article is concerned with conjugacy problems arising in homeomorphisms group, Hom($F$), of unbounded subsets $F$ of normed vector spaces $E$. Given two homeomorphisms $f$ and $g$ in Hom($F$), it is shown how the existence of a…

We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a…

A generalized cusp $C$ is diffeomorphic to $[0,\infty)$ times a closed Euclidean manifold. Geometrically $C$ is the quotient of a properly convex domain by a lattice, $\Gamma$, in one of a family of affine groups $G(\psi)$, parameterized by…

Two knots are homology concordant if they are smoothly concordant in a homology cobordism. The group $\hat{\mathcal{C}}_{\mathbb{Z}}$ (resp. $\mathcal{C}_{\mathbb{Z}}$) was previously defined as the set of knots in homology spheres that…