Related papers: The Chern Character in the Simplicial de Rham Comp…

By a theorem of Bernhard Keller the de Rham cohomology of a smooth variety is isomorphic to the periodic cyclic homology of the differential graded category of perfect complexes on the variety. Both the de Rham cohomology and the cyclic…

We propose some conditions on a poset that produce a small chain complex for its homology. This allows to compare simplicial complexes and Quillen's complexes under the same prism. It turns out they differ in the existence or not of free…

We show that the characteristic polynomial of a hyperplane arrangement can be recovered from the class in the Grothendieck group of varieties of the complement of the arrangement. This gives a quick proof of a theorem of Orlik and Solomon…

Let $\mathcal{F}$ be a coherent sheaf on a complex variety $X$ that has a locally free resolution $E^{\bullet}$. In [19], the authors constructed a pseudomeromorphic current whose support is contained in $supp(E^{\bullet})$ that represents…

In this note, we investigate the Chern classes of flat bundles in the arithmetic Deligne Cohomology, introduced by Green-Griffiths, Asakura-Saito. We show nontriviality of the Chern classes in some cases and the proof also indicates that…

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 give a generalisation of the character formula of Deligne--Lusztig representations from the finite field case to the truncated formal power series case. Motivated by this generalisation, we give a definition of Green functions for these…

We introduce Chern classes in $U(m)$-equivariant homotopical bordism that refine the Conner-Floyd-Chern classes in the $MU$-cohomology of $B U(m)$. For products of unitary groups, our Chern classes form regular sequences that generate the…

We prove that Chern classes in continuous $\ell$-adic cohomology of automorphic bundles associated to representations of $G$ on a projective Shimura variety with data $(G,X)$ are trivial rationally. It is a consequence of Beilinson's…

We derive simple explicit formulas for the character of a cycle in the Connes' (b,B)-bicomplex of cyclic cohomology and give applications to the Fredholm modules and equivariant characteristic classes.

We use flat antiholomorphic superconnections to study orbifold Chern character following the method introduced by Bismut, Shen, and Wei. We show the uniqueness of orbifold Chern character by proving a Riemann-Roch-Grothendieck theorem for…

We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the…

In this note we consider the symplectic reduction of a four-dimensional holomorphic Chern-Simons theory recently introduced in arXiv:1908.02289 for describing integrable field theories. We work out explicitly the case of the lambda deformed…

We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semifinite spectral triple recovers the Connes-Moscovici cyclic…

We construct a functorial decomposition of de Rham cohomology sheaves, called weight decomposition, for smooth analytic spaces over non-Archimedean fields embeddable into $\mathbf{C}_p$, which generalizes a construction of Berkovich and…

General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for…

In this paper we are begining to explore the complex counterpart of the Chern-Simon-Witten theory. We define the complex analogue of the Gauss linking number for complex curves embedded in a Calabi-Yau threefold using the formal path…

For Y a closed normal subvariety of codimension c of a smooth complex variety X, Brylinski and Kashiwara showed that the local cohomology module H^c_Y(X,O_X) contains a unique simple D_X-submodule, denoted by L(Y,X). In this paper the…

We construct chain-level $S^1$-equivariant string topology for each simply connected closed manifold. This amounts to constructing a Maurer-Cartan element for the canonical involutive Lie bialgebra (IBL) structure on the dual cyclic bar…

We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working…