Related papers: The Behavior of Nil-Groups under Localization and …

Loday's assembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalization that places both ingredients on the same footing. Building on…

We consider possibly singular rational projective k*-surfaces and provide an explicit description of the unit component of the automorphism group in terms of isotropy group orders and intersection numbers of suitable invariant curves. As an…

We study Chern characters and the assembly mapping for free actions using the framework of geometric $K$-homology. The focus is on the relative groups associated with a group homomorphism $\phi:\Gamma_1\to \Gamma_2$ along with applications…

Let $G=C_{p^n}$ be a finite cyclic p-group, and let $Hol(G)$ denote its holomorph. In this work, we find and characterize the regular subgroups of $Hol(G)$ that are mutually normalizing each other in the permutation group $Sym(G)$. We…

Based on the localization algebras of Yu, and their subsequent analysis by Qiao and Roe, we give a new picture of KK-theory in terms of time-parametrized families of (locally) compact operators that asymptotically commute with appropriate…

Let $F$ be a nonarchimedean local field of characteristic zero and let SL(N) = SL(N,F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the $K$-theory. We provide full arithmetic details. This…

Let A a regular F_p-algebra. The relative K-groups K_q(A[x]/(x^m),(x)) and the Nil-groups Nil_q(A[x]/(x^m)) were evaluated earlier by the author and Madsen in terms of the big de Rham-Witt groups of the ring A. In this paper, we evaluate…

Following Plotkin we say that the automorphism $x$ of the group $G$ is a nil-automorphism if, for every $g\in G$, there exists $n=n(g)$ such that $[g,_n x]=1$. If the integer $n$ can be chosen independently of $g$, then $x$ is said to be…

Let f: X -> Y be a based map of simply connected spaces. The corresponding evaluation map w: map(X,Y;f) -> Y induces a homomorphism of homotopy groups whose image in pi_n(Y) is called the nth evaluation subgroup of f. The nth Gottlieb group…

Controlled $K$-theory is used to show that algebraic $K$-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite…

Let $V_r(\Sigma)$ be the generalised Thompson group defined as the automorphism group of a valid, bounded, and complete Cantor algebra. We show that that for every $n>0$ there is a $k>n,$ such that there exists a $k$-dimensional…

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…

We study dilations of finite tuples of normal, completely positive and completely contractive maps (which we call CP-maps) acting on a von Neumann algebra, and commuting according to a graph G. We show that if G is acyclic, then a tuple…

The notion of a cyclic map g: A -> X is a natural generalization of a Gottlieb element in pi_n(X). We investigate cyclic maps from a rational homotopy theory point of view. We show a number of results for rationalized cyclic maps which…

The concept of well group in a special but important case captures homological properties of the zero set of a continuous map $f:K\to R^n$ on a compact space K that are invariant with respect to perturbations of f. The perturbations are…

We study a relative variant of Serre's notion of $G$-complete reducibility for a reductive algebraic group $G$. We let $K$ be a reductive subgroup of $G$, and consider subgroups of $G$ which normalise the identity component $K^{\circ}$. We…

The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map…

We consider a class of so-called ring $Q$-mappings that are a generalization of quasiconformal mappings. Theorems on the local behavior of inverse maps of this class are obtained. Under certain conditions, we also investigated the behavior…

We introduce a class of rings, namely the class of left or right $p$-nil rings, for which the adjoint groups behave regularly. Every $p$-ring is close to being left or right $p$-nil in the sense that it contains a large ideal belonging to…

For a locally finite connected graph $X$ we consider the group $Maps(X)$ of proper homotopy equivalences of $X$. We show that it has a natural Polish group topology, and we propose these groups as an analog of big mapping class groups. We…