Related papers: On finitely summable Fredholm modules from Smale s…

A fundamental ingredient in the noncommutative geometry program is the notion of KK-duality, often called K-theoretic Poincar\'{e} duality, that generalises Spanier-Whitehead duality. In this paper we construct a $\theta$-summable Fredholm…

Motivated by classical facts concerning closed manifolds, we introduce a strong finiteness property in K-homology. We say that a C*-algebra has uniformly summable K-homology if all its K-homology classes can be represented by Fredholm…

We give a complete classification (up to smooth homotopy) of finitely summable Fredholm representations (Fredholm modules) over higher rank groups and lattices. Our results are a direct consequence of work of Bader, Furman, Gelander and…

We produce a variety of odd bounded Fredholm modules and odd spectral triples on Cuntz-Krieger algebras by means of realizing these algebras as "the algebra of functions on a non-commutative space" coming from a sub shift of finite type. We…

We provide results on the smoothness of normalisers in connected reductive algebraic groups $G$ over fields $k$ of positive characteristic $p$. Specifically we we give bounds on $p$ which guarantee that normalisers of subalgebras of…

We study homological invariants of \'etale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology…

We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C*-algebras. We prove that every K-homology class for such an algebra is represented by a Fredholm module having finite-rank…

We apply our previous work on the relation between groupoid homology and K-theory to Smale spaces. More precisely, we consider the unstable equivalence relation of a Smale space with totally disconnected stable sets, and prove that the…

Let $\sigma$ be the involution of the Roe algebra $\Roe{\RR}$ which is induced from the reflection $\RR\to\RR; x\mapsto -x$. A graded Fredholm module over a separable $C^*$-algebra $A$ gives rise to a homomorphism…

We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen--Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological…

Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi stable real (or complex) Frechet algebras.

Complete, conformally flat metrics of constant positive scalar curvature on the complement of $k$ points in the $n$-sphere, $k \ge 2$, $n \ge 3$, were constructed by R\. Schoen [S2]. We consider the problem of determining the moduli space…

We use techniques of Alper-Hall-Rydh to prove a local structure theorem for smooth morphisms between smooth stacks around points with linearly reductive stabilizers. This implies that the good moduli space of a smooth stack over a base has…

We compute the (stable) \'etale cohomology of $\mathrm{Hom}_{n}(C, \mathcal{P}(\vec{\lambda}))$, the moduli stack of degree $n$ morphisms from a smooth projective curve $C$ to the weighted projective stack $\mathcal{P}(\vec{\lambda})$, the…

We generalize to quantum weighted projective spaces in any dimension previous results of us on K-theory and K-homology of quantum projective spaces `tout court'. For a class of such spaces, we explicitly construct families of Fredholm…

This is a sequel to the paper [Cas]. Here, we extend the methods of Farb-Wolfson using the theory of FI_G-modules to obtain stability of equivariant Galois representations of the etale cohomology of orbit configuration spaces. We establish…

Kasparov $KK$-groups $KK(A,B)$ are represented as homotopy groups of the Pedersen-Weibel nonconnective algebraic $K$-theory spectrum of the additive category of Fredholm $(A,B)$-bimodules for $A$ and $B$, respectively, a separable and…

Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections on a principal G-bundle on a closed Riemann surface, and…

The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which…

In this article, we study the behaviour of smooth algebra $R$ over local Noetherian local ring $A$. At first, we observe that for every $f\in R$, $R_f$ has finite length in the category of $D(R,A)$-module if dimension of $A$ is zero. This…