Related papers: Twisted Spectra Revisited

A vertex algebra with an action of a group $G$ comes with a notion of $g$-twisted modules, forming a $G$-crossed braided tensor category. For a Lie group $G$, one might instead wish for a notion of $(\mathrm{d}+A)$-twisted modules for any…

It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras…

We study $4D$ $\mathcal{N}=2$ superconformal field theories that arise as the compactification of the six-dimensional $(2,0)$ theory of type $E_6$ on a punctured Riemann surface in the presence of $\mathbb{Z}_2$ outer-automorphism twists.…

The $A(\inft)$-algebra structure in homology of a DG-algebra is constructed. This structure is unique up to isomorphism of $A(\infty)$ algebras. Connection of this structure with Massey products is indicated. The notion of…

We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…

The moire flat bands in twisted bilayer graphene have attracted considerable attention not only because of the emergence of correlated phases but also due to their nontrivial topology. Specifically, they exhibit a new class of topology that…

We initiate the study of deformation theory in the context of derived and higher log geometry. After reconceptualizing the "exactification"-procedures in ordinary log geometry in terms of Quillen's approach to the cotangent complex, we…

We give an alternative treatment of the foundations of parametrized spectra, with an eye toward applications in fixed-point theory. We cover most of the central results from the book of May and Sigurdsson, sometimes with weaker hypotheses,…

We introduce a new type of categorical object called a \emph{hom-tensor category} and show that it provides the appropriate setting for modules over an arbitrary hom-bialgebra. Next we introduce the notion of \emph{hom-braided category} and…

We describe complex twistor spaces over inner 3-symmetric spaces $G/H$, such that $H$ acts transitively on the fibre. Like in the symmetric case, these are flag manifolds $G/K$ where $K$ is the centralizer of a torus in $G$. Moreover, they…

In the paper "Deformation theory of abelian categories", the last two authors proved that an abelian category with enough injectives can be reconstructed as the category of finitely presented modules over the category of its injective…

We study deformation of tube algebra under twisting of graded monoidal categories. When a tensor category $\mathcal{C}$ is graded over a group $\Gamma$, a torus-valued 3-cocycle on $\Gamma$ can be used to deform the associator of…

We study the notion of $1$-twisted semi-homogeneous vector bundles on $\mathbb{G}_m$-gerbes over abelian varieties, and classify point objects in the twisted derived categories of abelian varieties. As an application, we classify the…

Stacks were introduced by Grothendieck and Giraud and are, roughly speaking, sheaves of categories. Kashiwara developed the theory of twisted modules, which are objects of stacks locally equivalent to stacks of modules over sheaves of…

Given a torus bundle $Y$ over the circle and a cohomology class $[\omega]\in H^2(Y;\mathbb{Z})$ which evaluates nontrivially on the fiber, we compute the Heegaard Floer homology of $Y$ with twisted coefficients in the universal Novikov…

We develop the theory of derived differential geometry in terms of bundles of curved $L_\infty[1]$-algebras, i.e. dg manifolds of positive amplitudes. We prove the category of derived manifolds is a category of fibrant objects. Therefore,…

In this paper we study the dg-category of twisted perfect complexes on a ringed space with soft structure sheaf. We prove that this dg-category is quasi-equivalent to the dg-category of complexes of vector bundles on that space. This result…

We define and study twisted support varieties for modules over an Artin algebra, where the twist is induced by an automorphism of the algebra. Under a certain finite generation hypothesis, we show that the twisted variety of a module…

We construct new topological theories related to sigma models whose target space is a seven dimensional manifold of G_2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the…

We introduce a theory of twisted simplicial distributions on simplicial principal bundles, which allow us to capture Bell's non-locality, and the more general notion of quantum contextuality. We leverage the classical theory of simplicial…