Related papers: Coarse and equivariant co-assembly maps

In this paper, we establish a precise connection between higher rho invariants and delocalized eta invariants. Given an element in a discrete group, if its conjugacy class has polynomial growth, then there is a natural trace map on the…

In the present paper, we discuss applications of the derived completion theorems proven in our previous two papers. One of the main applications is to Riemann-Roch problems for forms of higher equivariant K-theory, which we are able to…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

In this paper we show that if two central simple $k$-algebras generate the same cyclic subgroup in $\mathrm{Br}(k)$, then there are rational maps between varieties associated to these algebras, such as Brauer--Severi varieties, norm…

We present a geometric proof of Bernstein's second adjointness for a reductive $p$-adic group. Our approach is based on geometry of the wonderful compactification and related varieties. Considering asymptotic behavior of a function on the…

We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas- invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of…

The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps…

Let $K$ be a simply connected compact Lie group and $T^{\ast}(K)$ its cotangent bundle. We consider the problem of "quantization commutes with reduction" for the adjoint action of $K$ on $T^{\ast}(K).$ We quantize both $T^{\ast}(K)$ and the…

Let $G_{\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\mathbb{R}}$ and assume that ${\rm rank}(G_\mathbb{R})={\rm rank}(K_\mathbb{R})$. For any representation $X$ of Gelfand-Kirillov dimension $\frac{1}{2}…

The Guillemin-Sternberg conjecture states that "quantisation commutes with reduction" in a specific technical setting. So far, this conjecture has almost exclusively been stated and proved for compact Lie groups $G$ acting on compact…

We revisit the construction of signature classes in C*-algebra K-theory, and develop a variation that allows us to prove equality of signature classes in some situations involving homotopy equivalences of noncompact manifolds that are only…

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…

We prove uniqueness of equivariant harmonic maps into irreducible symmetric spaces of non-compact type and Euclidean buildings associated to isometric actions by Zariski dense subgroups.

We introduce a slight modification of the usual equivariant $KK$-theory. We use this to give a $KK$-theoretical proof of an equivariant index theorem for Dirac-Schrodinger operators on a non-compact manifold of nowhere positive curvature.…

We construct the coarse index class with support condition (as an element of coarse $K$-homology) of an equivariant Dirac operator on a complete Riemannian manifold endowed with a proper, isometric action of a group. We further show a…

We give an axiomatic characterization of maps from algebraic K-theory. The results apply to a class of maps from algebraic K-theory to any suitable cohomology theory or to algebraic K-theory, which includes all group morphisms. In…

The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real…

We give a new proof of the universal property of $KK^G$-theory with respect to stability, homotopy invariance and split-exactness for $G$ a locally compact group, or a locally compact (not necessarily Hausdorff) groupoid, or a countable…

We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichm\"uller theory, with a focus on rank $2$ Hitchin components.…

In this paper, we construct an equivariant coarse homology theory with values in the category of non-commutative motives of Blumberg, Gepner and Tabuada, with coefficients in any small additive category. Equivariant coarse K-theory is…