相关论文: Factorization homology of stratified spaces

We refine the intersection product in homology to an equivariant setting, which unifies several known constructions. As an application, we give a common generalisation of the Chas-Sullivan string product on a manifold and the…

The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…

We develop a method of quantization for free field theories on manifolds with boundary where the bulk theory is topological in the direction normal to the boundary and a local boundary condition is imposed. Our approach is within the…

We consider a sheaf of exterior algebras on a simplicial poset $S$ and introduce a notion of homological characteristic function. Two natural objects are associated with these data: a graded sheaf $\mathcal{I}$ and a graded cosheaf…

We announce recent results on a connection between factorization statistics of polynomials over a finite field and the structure of the cohomology of configurations in $\mathbb{R}^3$ as a representation of the symmetric group. This…

In the case of toric varieties, we continue the pursuit of Kontsevich's fundamental insight, Homological Mirror Symmetry, by unifying it with the Mori program. We give a refined conjectural version of Homological Mirror Symmetry relating…

The tools and arguments developed by Kevin Costello are adapted to families of "Outer Spaces" or spaces of graphs. This allows us to prove a version of Deligne's conjecture: the Harrison homology associated to a homotopy commutative algebra…

We construct decompositions of: (1) the cohomology of smooth stacks, (2) the Borel--Moore homology of $0$-shifted symplectic stacks, and (3) the vanishing cycle cohomology of $(-1)$-shifted symplectic stacks, assuming a good moduli space…

Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…

J. Przytycki has established a connection between the Hochschild homology of an algebra $A$ and the chromatic graph homology of a polygon graph with coefficients in $A$. In general the chromatic graph homology is not defined in the case…

In a previous work we showcased the factorization method to find the symmetries of superintegrable systems with spherical separability in flat spaces. Here we analyze the same problem, but in constant curvature spaces along the examples of…

For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…

We define a simplicial category called the category of derived manifolds. It contains the category of smooth manifolds as a full discrete subcategory, and it is closed under taking arbitrary intersections in a manifold. A derived manifold…

For commutative algebras there are three important homology theories, Harrison homology, Andre-Quillen homology and Gamma-homology. In general these differ, unless one works with respect to a ground field of characteristic zero. We show…

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…

In a previous paper, Sarkar and the third author gave a combinatorial description of the hat version of Heegaard Floer homology for three-manifolds. Given a cobordism between two connected three-manifolds, there is an induced map between…

Given an isolated, quasi-homogeneous singularity $X$ we prove that there is a group isomorphism between the group of rank one reflexive sheaves on $X$ and the free abelian group generated by $\mathbb{C}^*$-divisors, modulo linear…

Let M,N and B\subset N be compact smooth manifolds of dimensions n+k,n and \ell, respectively. Given a map f from M to N, we give homological conditions under which g^{-1}(B) has nontrivial cohomology (with local coefficients) for any map g…

The theory of abelian categories proved very useful, providing an axiomatic framework for homology and cohomology of modules over a ring and, in particular, of abelian groups. For many years, a similar categorical framework has been lacking…

Homology is characterized by the Eilenberg-Steenrod axioms. We define homology of higher categories via a categorical analogue of the Eilenberg-Steenrod axioms. We prove a categorical Dold-Kan correspondence, providing a combinatorial…