Related papers: Atiyah and Todd classes arising from integrable di…

Given a compact Lie group $G$ acting on a space $X$, the classical Atiyah-Segal completion theorem identifies topological $K$-theory of the homotopy quotient $X/G$ with an explicit completion of $G$-equivariant topological $K$-theory of…

We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold…

We prove a tamely ramified version of the Kazhdan-Lusztig equivalence using factorization algebras. More precisely, we establish an equivalence between the DG category of Iwahori-integrable affine Lie algebra representations and the DG…

For a complete toric variety, we obtain an explicit formula for the localized equivariant Todd class in terms of the combinatorial data -- the fan. This is based on the equivariant Riemann-Roch theorem and the computation of the equivariant…

We introduce and study a special class of Kato manifolds, which we call toric Kato manifolds. Their construction stems from toric geometry, as their universal covers are open subsets of toric algebraic varieties of non-finite type. This…

The Steinitz class of a number field extension K/k is an ideal class in the ring of integers O_k of k, which, together with the degree [K:k] of the extension determines the O_k-module structure of O_K. We call rt(k,G) the classes which are…

The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By…

The $\imath$Hall algebra of a weighted projective line is defined to be the semi-derived Ringel-Hall algebra of the category of $1$-periodic complexes of coherent sheaves on the weighted projective line over a finite field. We show that…

We compute the eta function $\eta(s)$ and its corresponding $\eta$-invariant for the Atiyah-Patodi-Singer operator $\mathcal{D}$ acting on an orientable compact flat manifold of dimension $n =4h-1$, $h\ge 1$, and holonomy group $F\simeq…

The purpose of this article is to show that flat compact K\"ahler manifolds exhibit the structure of a Frobenius manifold, a structure originating in 2D Topological Quantum Field Theory and closely related to Joyce structure. As a result,…

In this note we survey Hodge-theoretic formulae of Atiyah-Meyer type for genera and characteristic classes of complex algebraic varieties, and derive some new and interesting applications. We also present various extensions to the singular…

We give the first examples of smooth projective varieties $X$ over a finite field $\mathbb{F}$ admitting a non-algebraic torsion $\ell$-adic cohomology class of degree $4$ which vanishes over $\overline{\mathbb{F}}$. We use them to show…

The equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group. We prove that toric manifolds (i.e. compact smooth toric varieties) are…

Since the work of Mikhail Kapranov in [Kap], it is known that the shifted tangent complex $\mathbb{T}_X[-1]$ of a smooth algebraic variety $X$ is endowed with a weak Lie structure. Moreover any complex of quasi-coherent sheaves on $X$ is…

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…

Let $A$ be a star product on a symplectic manifold $(M,\omega_0)$, $\frac{1}{t}[\omega]$ its Fedosov class, where $\omega$ is a deformation of $\omega_0$. We prove that for a complex polarization of $\omega$ there exists a commutative…

For two representations of some local division algebra, congruent modulo $l$, giving rise to two Harris-Taylor local systems on the corresponding Newton strata of the special fiber of a KHT Shimura varieties, we prove that the $l$-torsion…

We present the Julia package ToricAtiyahBott.jl, providing an easy way to perform the Atiyah-Bott formula on the moduli space of genus $0$ stable maps $\overline{M}_{0,m}(X,\beta)$ where $X$ is any smooth projective toric variety, and…

Given a simply connected manifold M such that its cochain algebra, C^\star(M), is a pure Sullivan dga, this paper considers curved deformations of the algebra C_\star({\Omega}M) and consider when the category of curved modules over these…

We define a class of non-compact Fano toric manifolds, called admissible toric manifolds, for which Floer theory and quantum cohomology are defined. The class includes Fano toric negative line bundles, and it allows blow-ups along fixed…