Related papers: Relative Chern character, boundaries and index for…

A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian…

We study the mixed topological / holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold $(\Sigma\times{\mathbb C})/{\mathbb Z}_2$, obtaining a description of lattice integrable systems in the presence of a boundary.…

Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index problem for this class of operators. The solution is…

We extend the relative index theorem on non-compact manifolds to encompass a wide variety of hypoelliptic differential operators of arbitrary order, demonstrating that the change in index when changing a differential operator locally can be…

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities.…

We propose a categorification of the Chern character that refines earlier work of To\"en and Vezzosi and of Ganter and Kapranov. If X is an algebraic stack, our categorified Chern character is a symmetric monoidal functor from a category of…

For an additive Waldhausen category linear over a ring $k$, the corresponding $K$-theory spectrum is a module spectrum over the $K$-theory spectrum of $k$. Thus if $k$ is a finite field of characteristic $p$, then after localization at $p$,…

We study a natural family of non-local elliptic boundary problems on a compact oriented surface $\Sigma$ parametrized by the moduli space $\mathcal{M}_\Sigma$ of flat $G$-connections with framing along $\partial \Sigma$. This family…

Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra $\Psi^0(G)$ of pseudodifferential operators on some Lie groupoid $G$? If it could, the kernel ${\mathcal G}$ of the principal symbol homomorphism…

We construct a Chern character map from the K-theory of the reduced C^* algebra of the p-adic GL(n) with values in the periodic cyclic homology of the Schwartz algebra of this group. We prove that this map is an isomorphism after tensoring…

In this paper, we continue our program of systematic categorification of the Noncommutative Differential Geometry of Connes. We replace a ring with a small $\mathbb C$-linear category, seen as a ring with several objects in the sense of…

We study the geometry and topology of (filtered) algebra-bundles ${\bf\Psi}^{\mathbb Z}$ over a smooth manifold $X$ with typical fibre $\Psi^{\mathbb Z}(Z; V)$, the algebra of classical pseudodifferential operators of integral order on the…

We consider compact homogeneous spaces G/H of positive Euler characteristic endowed with an invariant almost complex structure J and the canonical action \theta of the maximal torus T ^{k} on G/H. We obtain explicit formula for the…

We study the quantization of spaces whose K-theory in the classical limit is the ring of dual numbers $\mathbb{Z}[t]/(t^2)$. For a compact Hausdorff space we recall necessary and sufficient conditions for this to hold. For a compact quantum…

We study a family of pseudodifferential operators (quantum Hamiltonians) on $L^{2}(\mathbb{R}^{n};\mathbb{C}^{d})$ whose spectrum exhibits two energy bands exchanging a finite number of eigenvalues. We show that this number coincides with…

We study the essential spectrum and Fredholm properties of integral and pseudodiferential operators associated to (maybe non-commutative) locally compact groups G. The techniques involve crossed product C*-algebras. We extend previous…

For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…

We present an operator-coefficient version of Sato's infinite-dimensional Grassmann manifold, and tau-function. In this context, the Burchnall-Chaundy ring of commuting differential operators becomes a C*-algebra, to which we apply the…

For a manifold with boundary, the restriction of Chern's transgression form of the Euler curvature form over the boundary is closed. Its cohomology class is called the secondary Chern-Euler class and used by Sha to formulate a relative…

Let X be the quasi-projective symplectic surface that is given by the total space of the invertible sheaf O(-2) over the projective line. Let Hilb X be the family of Hilbert schemes of points on X. We give and prove a closed formula…