Related papers: $G$-crossed braided zesting

Let $G$ be a finite group, and let $X$ be a smooth, orientable, connected, closed 4-dimensional $G$-manifold. Let $\mathcal{S}$ be a smooth, embedded, $G$-invariant surface in $X$. We introduce the concept of a $G$-equivariant trisection of…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

Let $G$ be a group and $X$ be a $G$-space. A subset $F$ of $X$ is called a kaleidoscopical configuration if there exists a surjective coloring $\chi:X\to Y$ such that the restriction of $\chi$ on each subset $gF$, $g\in G$ is a bijection.…

In this work, we analyze the structure of the category of partial representations of a finite group $G$ as a multifusion category, providing an alternative way to describe simple objects and their tensor products. We describe the…

We define unbounded twisted complexes and bicomplexes generalising the notion of a (bounded) twisted complex over a DG category [BK90]. These need to be considered relative to another DG category $B$ admitting countable direct sums and…

We define a "mirror version" of Brzezinski's crossed product and we prove that, under certain circumstances, a Brzezinski crossed product D\otimes_{R, \sigma}V and a mirror version W\bar{\otimes}_{P, \nu}D may be iterated, obtaining an…

In this paper we study twisted complexes on a ringed space and prove that it gives a new dg-enhancement of the derived category of perfect complexes on that space. A twisted complex is a collection of locally defined sheaves together with…

Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A multi-crossing is a crossing where more than two strands meet at a single point, such that each strand bisects the…

We classify all fusion categories for a given set of fusion rules with three simple object types. If a conjecture of Ostrik is true, our classification completes the classification of fusion categories with three simple object types. To…

Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product C$^*$-algebra $C(G)\rtimes\Z$ obtained from a translation on $G$ by a generator of a dense cyclic subgroup.…

We give two proofs of a level-rank duality for braided fusion categories obtained from quantum groups of type $C$ at roots of unity. The first proof uses conformal embeddings, while the second uses a classification of braided fusion…

The anomaly of non-invertible higher-form symmetries is determined by the braiding of topological operators implementing them. In this paper, we study a method to classify braidings on topological line and surface operators by leveraging…

Given groupoids $G$ and $H$ and a $(G,H)$-equivalence $X$ we may form the transformation groupoid $G\ltimes X\rtimes H$. Given a separable groupoid dynamical system $(A,G\ltimes X\rtimes H,\omega)$ we may restrict $\omega$ to an action of…

The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…

It is shown that every $2$-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra $A$ defines a very explicit infinitesimal $2$-braiding on the homotopy $2$-category of the symmetric monoidal…

Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…

The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some…

This paper is a sequel to "T-structures and twisted complexes on derived injectives" by the same author with W. Lowen and M. Van den Bergh. We define a dg-category of unbounded twisted complexes on a dg-category, which is particularly…

We investigate a new lattice of generalised non-crossing partitions, constructed using the geometry of the complex reflection group $G(e,e,r)$. For the particular case $e=2$ (resp. $r=2$), our lattice coincides with the lattice of simple…

A family of TQFTs parametrised by G-crossed braided spherical fusion categories has been defined recently as a state sum model and as a Hamiltonian lattice model. Concrete calculations of the resulting manifold invariants are scarce because…