相关论文: Chern character for twisted complexes
We show that every set of numbers that occurs as the set of Chern numbers of an almost complex manifold $M^{2n}$, $n\geqslant 3$, may be realized as the set of Chern numbers of a connected almost complex manifold with an almost complex…
The Chern character maps are one of the most important working tools in mathematics. Although they admit numerous different constructions, they are not yet fully understood at the conceptual level. In this note we eliminate this gap by…
The goal of this paper is to study the Chern classes of coherent sheaves (and more generally perfect complexes) that admit crystal structures in the setting of crystalline cohomology and more generally relative prismatic cohomology. In the…
We show that the second Chern character of any projective toric manifold of Picard number three is not ample. In connection with this result, we give various examples of the positivity of higher Chern characters of projective toric…
We present a solution of the generalized Hirzebruch problem on the relations between the Chern numbers of a stably almost complex manifold and the Chern numbers of its virtual Chern submanifolds.
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 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…
We calculate the parabolic Chern character of a bundle with locally abelian parabolic structure on a smooth strict normal crossings divisor, using the definition in terms of Deligne-Mumford stacks. We obtain explicit formulas for $ch_1$,…
Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral…
On the basis of Dupont's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Chern character. We also prove the related conjecture due to Brylinski. This gives a way to construct a cocycle in a local truncated…
Following Bloch-Esnault-Kerz and Green-Griffiths' recent works on deformation of algebraic cycle classes, we use Chern character from K-theory to negative cyclic homology to show how to eliminate obstructions to deforming cycles.
We define an index of a collection of 1-forms on a complex isolated complete intersection singularity corresponding to a Chern number and, in the case when the 1-forms are complex analytic, express it as the dimension of a certain algebra.
This paper surveys topological results obtained from characteristic classes built from the two types of traces on the algebra of pseudodifferential operators of nonpositive order. The main results are the construction of a universal $\hat…
For a two-periodic complex of vector bundles, Polishchuk and Vaintrob have constructed its localized Chern character. We explore some basic properties of this localized Chern character. In particular, we show that the cosection localization…
In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable $C^*$-algebra by a twisted $\mathbb{R}^d$-action. The…
There is a well developed intersection theory on smooth Artin stacks with quasi-affine diagonal. However, for Artin stacks whose diagonal is not quasi-finite the notion of the degree of a Chow cycle is not defined. In this paper we propose…
Assuming the existence of the perfect crystal bases of Kirillov-Reshetikhin modules over simply-laced quantum affine algebras, we construct certain perfect crystals for twisted quantum affine algebras, and also provide compelling evidence…
We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex…
The Chern-Simons forms for R-linear connections on Lie algebroids are considered. A generalized Chern-Simons formula for such R-linear connections is obtained. We it apply to define Chern character and secondary characteristic classes for…
Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…