Related papers: A Simple Formula for Generating Chern Characters b…
We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel…
Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential boundary value problems and shift operators…
We first construct closed spherical CR manifolds of dimension at least five having non-trivial first Chern class with real coefficients. We next prove a constraint on Chern classes with real coefficients of (not necessarily closed)…
We calculate the equivariant motivic Chern class for configuration space of a quasiprojective (maybe singular) variety and the space of vectors with different directions. We prove the formulas for generating series of these classes. We…
A Chen generating series, along a path and with respect to $m$ differential forms,is a noncommutative series on $m$ letters and with coefficients which are holomorphic functionsover a simply connected manifold in other words a series with…
In this note we give a simple, model-independent construction of Chern classes as natural transformations from differential complex K-theory to differential integral cohomology. We verify the expected behaviour of these Chern classes with…
Let G be a complex connected reductive group. The representation ring R(G) admits a canonical filtration defined in terms of the lambda-structure. We compute the associated graded ring gr R(G) (over Q) and the Chern classes of a…
We prove the multiplicative property of localized Chern characters. As a direct consequence, a localized Chern character gives rise to a ring homomorphism from the K-group of periodic complexes to the bivariant Chow cohomology group. As an…
By using an approach of the invariant theory we obtain a new formula for the ordinary generating function of the numbers of the simple graphs with $n$ nodes.
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth…
In a previous article, we generalised the classical four-dimensional Chern-Gauss-Bonnet formula to a class of manifolds with finitely many conformally flat ends and singular points, in particular obtaining the first such formula in a…
We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological…
We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their…
We develop a novel and systematic approach to computing the $(2n-1)$-form Chern-Simons potential given the Pontryagin density, i.e. the $n^{\text{th}}$ Chern character, in arbitrary even dimensions $D=2 n \geq 2$. Throughout we work with a…
A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a…
We present two formulas for Chern classes of the tensor product of two vector bundles. In the first formula we consider a matrix containing Chern classes of the first bundle and we take a polynomial of this matrix with Chern classes of the…
In this work we show how the Multiplicity Polar Theorem can be used to calculate Chern numbers for a collection of 1-forms.
We study the category of matrix factorizations for an isolated hypersurface singularity. We compute the canonical bilinear form on the Hochschild homology of this category. We find explicit expressions for the Chern character and the…
Here we are fixing an output of a trivial calculation based on Konsevich's differential 2-form for the Chern class of polygon bundle. As a result an interesting combinatorics and arithmetics jumps right out of a jukebox. The calculation…