Related papers: Morphisms between spaces of leaves viewed as fract…
The well-known calculus of fractions of Gabriel and Zisman provides a convenient way to formally invert morphisms in a category. This was generalised to bicategories by Pronk. We extend these constructions by presenting a calculus of lax…
We introduce a graphical calculus for computing morphism spaces between the categorified spin networks of Cooper and Krushkal. The calculus, phrased in terms of planar compositions of categorified Jones-Wenzl projectors and their duals, is…
An isomorphism between two hermitian unitals is proved, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).
We introduce the concept of morphism of pseudogroups generalizing the \'etal\'e morphisms of Haefliger. With our definition, any continuous foliated map induces a morphism between the corresponding holonomy pseudogroups. The main theorem…
This is a survey concerning the relationship between Lie Groupoids (and their morphisms) and singular foliations in the sense of Sussmann-Stefan (considered from a purely geometrical point of view). We focus on the interaction between the…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…
The theory of categories of fractions as originally developed by Gabriel and Zisman is reviewed in a pedagogical manner giving detailed proofs of all statements. A weakening of the category of fractions axioms used by Higson is discussed…
A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in the paper arXiv:0803.3652 by the second author. Here we enhance the graphical calculus introduced and developed in that paper to include…
Hiss and Szczepa\'nski proved in 1991 that the holonomy group of any compact flat Riemannian manifold, of dimension at least two, acts reducibly on the rational span of the Euclidean lattice associated with the manifold via the first…
We introduce a notion of equivalence for singular foliations - understood as suitable families of vector fields - that preserves their transverse geometry. Associated to every singular foliation there is a holonomy groupoid, by the work of…
We provide some corrections and clarifications to the paper [Gr3] of the title. In particular, we clarify the "left/right" conventions on complex reflection groups and their braid groups. Most importantly, we fill in a gap related to the…
This paper contains corrections to Madea, Rosenberg, Torres-Ardila, "The Geometry of Loop Spaces II: Characteristic Classes," Advances in Math. (287), 2016, 485-518. The main change is that results about $\pi_1({\rm Diff}(M))$ are replaced…
We review the language of differential forms and their applications to Riemannian Geometry with an orientation to General Relativity. Working with the principal algebraic and differential operations on forms, we obtain the structure…
In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are…
We give an explicit description of the set of all factorization structures, or twisting maps, existing between the algebras k^2 and k^2, and classify the resulting algebras up to isomorphism. In the process we relate several different…
The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
We introduce new classes of right quaternionic Hilbert spaces of Bargmann-Fock type $\mathcal{GB}_{m}^{2}(\mathbb{H})$, labeled by nonnegative integer $m$, generalizing the so-called slice hyperholomorphic Bargmann-Fock space introduced…