Related papers: A regulator for smooth manifolds and an index theo…

Let $X/S$ be a smooth family of smooth projective varieties, where $S$ is a smooth affine curve over a field $k$ of characteristic $0.$ We relate the differential fundamental groupoid scheme of $X/k$ with the differential fundamental…

We study the index homomorphism of even K-groups arising from a class in even KK-theory via the Kasparov product. Due to the seminal work of Baaj and Julg, under mild conditions on the C^*-algebras in question such a class in KK-theory can…

Given any connected topological space $X$, assume that there exists an epimorphism $\phi: \pi_1(X) \to \mathbb{Z}$. The deck transformation group $\mathbb{Z}$ acts on the associated infinite cyclic cover $X^\phi$ of $X$, hence on the…

Coisotropic algebras are used to formalize coisotropic reduction in Poisson geometry as well as in deformation quantization and find applications in various other fields as well. In this paper we prove a Serre-Swan Theorem relating the…

We establish the stable homotopy classification of elliptic pseudodifferential operators on manifolds with corners and show that the set of elliptic operators modulo stable homotopy is isomorphic to the K-homology group of some stratified…

The Jacobian ring J(X) of a smooth hypersurface determines its isomorphism type. This has been used by Donagi and others to prove the generic global Torelli theorem for hypersurfaces in many cases. In Voisin's original proof of the global…

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…

The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild…

We construct analytically the signature operator for a new family of topological manifolds. This family contains the quasi-conformal manifolds and the topological manifolds modeled on germs of homeomorphisms of R^n possessing a derivative…

We compute the rational homology of the moduli stack $\mathcal{M}$ of objects in the derived category of certain smooth complex projective varieties $X$ including toric varieties, flag varieties, curves, surfaces, and some 3- and 4-folds.…

When the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the $K-$theory index. This result gives a concrete connection…

We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are…

We give a version of Gromov's compactess theorem for pseudoholomorphic curves in the case of quasiregular mappings between closed manifolds. More precisely we show that, given $K\ge 1$ and $D\ge 1$, any sequence $(f_n \colon M \to N)$ of…

We prove that all K-homology classes of the stable (and unstable) Ruelle algebra of a Smale space have explicit Fredholm module representatives that are finitely summable on the same smooth subalgebra and with the same degree of…

We construct the moduli space of smooth hypersurfaces with level $N$ structure over $\mathbb{Z}[1/N]$. As an application we show that, for $N$ large enough, the stack of smooth hypersurfaces over $\mathbb{Z}[1/N]$ is uniformisable by a…

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…

We show that for a smooth, projective variety X defined over a number field K, cyclic homology with coefficients in the ring of infinite adeles of K, provides the right theory to obtain, using the lambda-operations, Serre's archimedean…

We prove a Fredholm property for spin-c Dirac operators $\mathsf{D}$ on non-compact manifolds satisfying a certain condition with respect to the action of a semi-direct product group $K\ltimes \Gamma$, with $K$ compact and $\Gamma$…

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered…

We describe a map from the equivariant twisted K-homology of a compact, connected, simply connected Lie group $G$ to the Verlinde ring. Our map is described at the level of `D-cycles' for the geometric twisted K-homology of $G$, and is…