Related papers: The higher twisted index theorem for foliations

We have previously shown that the truncated Weil algebra of any Lie algebra is a Hopf-cyclic type complex with nontrivial coefficients. In this paper we apply this result to transfer the characteristic classes of transversely orientable…

In this paper we compute explicit formulas for the holonomy map for a gerbe with connection over an orbifold. We show that the holonomy descends to a transgression map in Deligne cohomology. We prove that this recovers both the inner local…

For any Lie groupoid we construct an analytic index morphism taking values in a modified $K-theory$ group which involves the convolution algebra of compactly supported smooth functions over the groupoid. The construction is performed by…

The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…

We construct twisted $\mathcal{D}$-modules on the projective line $\mathbb{P}^1$ that are equivariant for the action of the diagonal torus subgroup of $SL_2$. In the most interesting case these arise as extensions from local systems on…

We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the complex of differential forms on a symplectic manifold to the…

Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

In this paper we consider a family of Dirac-type operators on fibration $P \to B$ equivariant with respect to an action of an etale groupoid. Such a family defines an element in the bivariant $K$ theory. We compute the action of the…

We compare the higher analytic torsion of Bismut and Lott of a fibre bundle p: M -> B equipped with a flat vector bundle F -> M and a fibre-wise Morse function h on M with a higher torsion T that is constructed in terms of a families…

In earlier joint work with A. Connes on transverse index theory on foliations, cyclic cohomology adapted to Hopf algebras has emerged as a decisive tool in deciphering the total index class of the hypoelliptic signature operator. We have…

In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of…

Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…

Starting with a $\mathbb{C}^*$-valued cocycle on the global quotient orbifold $X // G$, we apply transgression techniques for 2-gerbes, as developed by Lupercio and Uribe, to construct a gerbe on the orbifold loop space $\mathcal{L}(X//G)$.…

We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator $D_m$ on the maximal Connes-Skandalis Hilbert module and…

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

This paper, together with Part II, expands the results of math.DG/9803051. In Part I we study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective…

We prove a general relative higher index theorem for complete manifolds with positive scalar curvature towards infinity. We apply this theorem to study Riemannian metrics of positive scalar curvature on manifolds. For every two metrics of…

We prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (ie. non-classical) twist of $K$-theory over $G=SU(n)$. This twist is represented…

We study the $S^1\times\Sigma_{\mathfrak g}$ topologically twisted index and the squashed sphere partition function of various 3d $\mathcal N\geq2$ holographic superconformal field theories arising from M2-branes. Employing numerical…

By applying Seifert's algorithm to a special alternating diagram of a link L, one obtains a Seifert surface F of L. We show that the support of the sutured Floer homology of the sutured manifold complementary to F is affine isomorphic to…