Related papers: The circular Delannoy category

Given a smooth 3-fold $Y$, a line bundle $L \to Y$, and a section $s$ of $L$ such that the vanishing locus of $s$ is a normal crossings surface $X$ with graph-like singular locus, we present a way to reconstruct the singularity category of…

We construct the rings of generalized differential operators on the ${\bf h}$-deformed vector space of ${\bf gl}$-type. In contrast to the $q$-deformed vector space, where the ring of differential operators is unique up to an isomorphism,…

A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a…

This article introduces pre-Hilbert $*$-categories: an abstraction of categories exhibiting "algebraic" aspects of Hilbert-space theory. Notably, finite biproducts in pre-Hilbert $*$-categories can be orthogonalised using the Gram-Schmidt…

The extension of majorization (also called the rearrangement ordering), to more general groups than the symmetric (permutation) group, is referred to as $G$-majorization. There are strong results in the case that $G$ is a reflection group…

Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic $K$-theory since around 1970. There is an abundance of new applications…

In this memoir we extend the theory of global pseudo-differential operators to the setting of arbitrary sub-Riemannian structures on a compact Lie group. More precisely, given a compact Lie group $G$, and the sub-Laplacian $\mathcal{L}$…

We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies with the…

The traditional approach of defining the fundamental group first and then constructing universal coverings works well only for the class of Poincar\' e spaces. For general spaces there were several attempts to define generalized coverings…

Topologists are sometimes interested in space-valued diagrams over a given index category, but it is tricky to say what such a diagram even is if we look for a notion that is stable under equivalence. The same happens in (homotopy) type…

Suppose that $G$ is a group, $H$ and $K$ are proper isomorphic central subgroups of $G$, and $\mathfrak{G}$ is an HNN-extension of $G$ with the associated subgroups $H$ and $K$. We prove necessary and sufficient conditions for…

Given a suitable functor T:C -> D between model categories, we define a long exact sequence relating the homotopy groups of any X in C with those of TX, and use this to describe an obstruction theory for lifting an object G in D to C.…

We define a super version of the Connes-Moscovici Hopf algebra, $\mathcal{H}_1$. For that, we consider the supergroup $G^s=Diff^+(\mathbb{R}^{1,1})$ of orientation preserving diffeomorphisms of the superline $\mathbb{R}^{1,1}$ and define…

Let G be the group preserving a nondegenerate sesquilinear form on a vector space V, and H a symmetric subgroup of G of the type G1 x G2. We explicitly parameterize the H-orbits in the Grassmannian of r-dimensional isotropic subspaces of V…

Let $I$ be an infinite set, $\{G_i:i\in I\}$ be a family of (topological) groups and $G=\prod_{i\in I} G_i$ be its direct product. For $J\subseteq I$, $p_{J}: G\to \prod_{j\in J} G_j$ denotes the projection. We say that a subgroup $H$ of…

Given a group $G$, we define suitable 2-categorical structures on the class of all small categories with $G$-actions and on the class of all small $G$-graded categories, and prove that 2-categorical extensions of the orbit category…

Let $\textup{H}_g$ be a genus $g$ handlebody and $\textup{MCG}_{2n}(\textup{T}_g)$ be the group of the isotopy classes of orientation preserving homeomorphisms of $\textup{T}_g=\partial\textup{H}_g$, fixing a given set of $2n$ points. In…

This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…

A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of…

We study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. We show the existence of a recollement of the above quotient category and it has the…