Related papers: Operator ideals and assembly maps in $K$-theory

A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory…

This article introduces a quantized chip-firing model with close connections to the theory of rational lattice paths and rational parking functions. Given a graph with a sink and positive integers a,b,c with gcd(a,b)=1, a set S of vertices…

For a pivotal finite tensor category $\mathcal{C}$ over an algebraically closed field $k$, we define the algebra $\mathsf{CF}(\mathcal{C})$ of class functions and the internal character $\mathsf{ch}(X) \in \mathsf{CF}(\mathcal{C})$ for an…

We continue the study of operator algebras over the $p$-adic integers, initiated in our previous work [1]. In this sequel, we develop further structural results and provide new families of examples. We introduce the notion of $p$-adic von…

Let G be a compact connected Lie group, and (M,\omega) a Hamiltonian G-space with proper moment map \mu. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the…

We give a complete solution, for discrete countable groups, to the problem of defining and computing a geometric pairing between the left hand side of the Baum-Connes assembly map, given in terms of geometric cycles associated to proper…

Let G be a connected real reductive group. Orbit integrals define traces on the group algebra of G. We introduce a construction of higher orbit integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra of…

In this paper we introduce a new decomposition of power-bounded operators, analogous to the Jacobs-deLeeuw-Glicksberg decomposition. This is done using so-called K\"ohler semigroups and the general theory of right topological compact…

We present the following reflexivity-like result concerning the automorphism group of the $C^*$-algebra B(H), H being a separable Hilbert space. Let $\phi:B(H)\to B(H)$ be a multiplicative map (no linearity or continuity is assumed) which…

Given a henselian pair $(R, I)$ of commutative rings, we show that the relative $K$-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace $K \to \mathrm{TC}$. This yields a…

The algebraic structure of iterated integrals has been encoded by Chen. Formally, it identifies with the shuffle and Lie calculus of Lyndon, Ree and Sch\"utzenberger. It is mostly incorporated in the modern theory of free Lie algebras.…

For a countable discrete group $G$, we construct a new and concrete model for the equivariant topological $K$-homology theory of $G$, which is defined for all $G$-actions, not just for proper $G$-actions. The construction of our model…

Let H_c be the rational Cherednik algebra of type A_{n-1} with spherical subalgebra U_c=eH_ce. Then U_c is filtered by order of differential operators with associated graded ring gr U_c=C[h + h*]^W, where W is the n-th symmetric group.…

Consider a proper, isometric action by a unimodular locally compact group $G$ on a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. Then an equivariant Dirac-type operator $D$ on $M$ under a suitable boundary condition has…

Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group $\mathbb{G}$ and 1-injectivity of…

We establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, we…

Ghostly ideals are among the most mysterious objects in coarse index theory. In this paper, we show that if a metric space $X$ with bounded geometry admits a coarse embedding into an $\ell^p$-space ($1 \le p < \infty$), then the canonical…

We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…

Let $\M$ be a von Neumann algebra with a faithful normal trace $\T$, and let $H^\infty$ be a finite, maximal, subdiagonal algebra of $\M$. Fundamental theorems on conjugate functions for weak$^*$\!-Dirichlet algebras are shown to be valid…

If O is a reduced operad in symmetric spectra, an O-algebra I can be viewed as analogous to the augmentation ideal of an augmented algebra. Implicit in the literature on Topological Andre-Quillen homology is that such an I admits a…