Related papers: On an index theorem by Bismut

We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove…

We give a direct proof that the Freed-Lott differential analytic index is well defined and a condensed proof of the differential Grothendieck-Riemann-Roch theorem. As a byproduct we also obtain a direct proof that the R/Z analytic index is…

In this paper we show an index theorem for gerbes

We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.

This paper proves an integral version of the Riemann-Roch theorem for surface bundles, comparing the standard cohomology classes with the cohomology classes coming from the symplectic group.

In this paper, we prove the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level.

In this lecture we review apprearance of the Riemann-Roch Theorem in classical function theory, Algebraic topology, in theory of pseudo-differential operators and finally in noncommutative geometry. We show also it usefulness in many…

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local…

We prove an analog of Gromov--Lawson type relative index theorems for K-homology classes.

Let X --> B be a proper submersion with a Riemannian structure. Given a differential K-theory class on X, we define its analytic and topological indices as differential K-theory classes on B. We prove that the two indices are the same.

We prove an index theorem for the quotient module of a monomial ideal. We obtain this result by resolving the monomial ideal by a sequence of Bergman space like essentially normal Hilbert modules.

We give an exposition of the Morse Index Theorem in the Riemannian case in terms of the Maslov index, following and expanding upon Arnold's seminal paper. We emphasize the symplectic arguments in the proof and aim to be as self-contained as…

In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.

We prove the Jones Index Theorem using the K-theory of a cluster $C^*$-algebra of the Riemann sphere with two boundary components.

In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.

We introduce a cohomology theory that classifies differential objects that arise from Picard-Vessiot theory, using the differential Hopf-Galois descent. To do this, we provide an explicit description of Picard-Vessiot theory in terms of…

We prove an index theorem for inhomogeneous differential operators satisfying the Rockland condition (hence hypoelliptic). This theorem extends an index theorem for contact manifolds by Van-Erp.

In this paper we prove a $K$-homology index theorem for the Toeplitz operators obtained from the multishifts of the Bergman space on several classes of egg-like domains. This generalizes our theorem with Douglas and Yu on the unit ball.

We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.