相关论文: Three themes in the work of Charles Ehresmann: Loc…
This paper attempts to relate some ideas of Grothendieck in his Esquisse d'un programme and some of the recent results on 2-dimensional topology and geometry. Especially, we shall discuss the Teichm\"uller theory, the mapping class groups,…
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…
This article is devoted to the study of a higher-dimensional generalisation of de Rham epsilon lines. To a holonomic $D$-module $M$ on a smooth variety $X$ and a generic tuple of $1$-form $(\nu_1,\dots,\nu_n)$, we associate a point of the…
In this PhD thesis we will discuss some aspects in Commutative Algebra which have interactions with Algebraic Geometry, Representation Theory and Combinatorics. In particular, in the first chapter we will focus on understanding when certain…
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…
We apply representation theory to study the homology of equivariant Dehn-fillings of a given finite, regular cover of a compact 3-manifold with boundary a torus. This yields a polynomial which gives the rank of the part of the homology…
We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived…
Broadly speaking the present is a homotopy complement to the book of Giraud, albeit in a couple of different ways. In the first place there is a representability theorem for maps to a topological champ (a.k.a. stack) and whence an extremely…
In this paper, a new higher Hochschild Complex is defined with an Iterated Integral map to locally model differential forms on the space of bigons on $M$. In particular, given the local data for a gerbe with structure 2-group given by a…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We generalize some of the classical results of graph chordality to…
Given a general finite group $G$, there are various finite categories whose cohomology theories are of great interests. Recently Balmer and Grodal gave some new characterizations of the groups of endotrivial modules, via \v{C}ech cohomology…
As we known, the {\it Seifert-Van Kampen theorem} handles fundamental groups of those topological spaces $X=U\cup V$ for open subsets $U, V\subset X$ such that $U\cap V$ is arcwise connected. In this paper, this theorem is generalized to…
In this thesis we present several original contributions to the study of: - DG categories and their invariants; - Neeman's well-generated (algebraic) triangulated categories; - Fomin-Zelevinsky's cluster algebras approach via representation…
Building on Schlessinger's work, we define a framework for studying geometric deformation problems which allows us to systematize the relationship between the local and global tangent and obstruction spaces of a deformation problem.…
This is an introduction to type theory, synthetic topology, and homotopy type theory from a category-theoretic and topological point of view, written as a chapter for the book "New Spaces for Mathematics and Physics" (ed. Gabriel Catren and…
A. Bak developed a combinatorial approach to higher $K$-theory, in which control is kept of the elementary operations involved, through paths and `paths of paths' in what he called a global action. The homotopy theory of these was developed…
This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…
We investigate algebraic and compositional properties of abstract multiway rewriting systems, which are archetypical structures underlying the formalism of the Wolfram model. We demonstrate the existence of higher homotopies in this class…
The article explores function terms within uniform theories. It examines the uniformity of these theories through an algebraic lens. The paper compares the uniformity of terms and predicates within axiom schemas. It demonstrates the…