Related papers: Chern characters in equivariant basic cohomology

Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of…

Let $D$ be a (generalized) Dirac operator on a non-compact complete Riemannian manifold $M$ acted on by a compact Lie group $G$. Let $v:M --> Lie(G)$ be an equivariant map, such that the corresponding vector field on $M$ does not vanish…

In "Chern classes for coherent sheaves", H.I. Green constructs Chern classes in de Rham cohomology of coherent analytic sheaves. We construct here a formal $(\infty,1)$-categorical framework into which we can place Green's work and…

Let $G$ be a compact, connected, and simply connected Lie group. A principal $G$-bundle over a manifold $X$, equipped with a connection, together with a positive-energy representation of the loop group $LG$, gives rise to a…

We show how characteristic classes determine equivariant prequantization bundles over the space of connections on a principal bundle. These bundles are shown to generalize the Chern-Simons line bundles to arbitrary dimensions. Our result…

This work establishes the geometric component of Deligne's longstanding program on refined Grothendieck-Riemann-Roch formulas expressed through determinants of cohomology. The approach relies on a newly developed universal category of Chern…

We give Chern-Weil definitions of the Maslov indices of bundle pairs over a Riemann surface \Sigma with boundary, which consists of symplectic vector bundle on \Sigma and a Lagrangian subbundle on \partial{\Sigma} as well as its…

In this article, we investigate an axiomatic approach introduced by Grivaux for the study of rational Bott-Chern cohomology, and use it in that context to define Chern classes of coherent sheaves. This method also allows us to derive a…

In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and…

On conformal manifolds of even dimension $n\geq 4$ we construct a family of new conformally invariant differential complexes. Each bundle in each of these complexes appears either in the de Rham complex or in its dual. Each of the new…

A differential geometric version of noncommutative topological index theorem is worked out for covariant star products on noncommutative vector bundles. For start, a noncommutative manifold is considered as a product space X = Y * Z,…

A strong from of invariance under a group G is manifested in a family over the classifying space BG. We advocate a differential-geometric avatar of BG when G is a Lie group. Applied to G-equivariant connections on smooth principal or vector…

We give an algebro-geometric construction of the Hitchin connection, valid also in positive characteristic (with a few exceptions). A key ingredient is a substitute for the Narasimhan-Atiyah-Bott K\"ahler form that realizes the Chern class…

There is a large mathematical literature on classical mechanics and field theory, especially on the relationship to symplectic geometry. One might think that the classical Chern-Simons theory, which is topological and so has vanishing…

Given a matrix factorization, we use the Atiyah class to give an algebraic Chern-Weil type construction to its Chern character; this allows us to realize the Chern character in an explicit way. It also generalizes the existing result to any…

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…

The $\bar{\partial}_{_{J}}$ operator over an almost complex manifold induces canonical connections of type $(0,1)$ over the bundles of $(p,0)$-forms. If the almost complex structure is integrable then the previous connections induce the…

The aim of this note is to point out that Chern characters can be computed using curvatures o ``super-connections up to homotopy'. We also present an application to the vanishing theorem for Lie algebroids which is at the origin of new…

We study fractional quantum Hall states with quasihole excitations, on Riemann surfaces of arbitrary genus. For configurations with $m$ quasiholes we construct a vector bundle above the $m$-th symmetric power of the curve so that the fiber…

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially…