Related papers: The Algebraic Theory of the Fundamental Germ
The fundamental germ is a generalization of $\pi_{1}$, first defined for laminations which arise through group actions in math.DG/0506270. In this paper, the fundamental germ is extended to any lamination having a dense leaf admitting a…
We associate to every algebraic number field a hyperbolic surface lamination and an external fundamental group: the latter a generalization of the fundamental germ that necessarily contains external (not first order definable) elements. The…
In this note, we investigate how different fundamental groups of presentations of a fixed algebra $A$ can be. For finitely many finitely presented groups $G_i$, we construct an algebra $A$ such that all $G_i$ appear as fundamental groups of…
This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.
This paper constructs a Weyl group of a fundamental sandwich algebra.
In this paper, we prove that the fundamental group of a simplicial complex is isomorphic to the algebraic fundamental group of its incidence algebra, and we derive some applications.
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
The main goal of this note is to provide a new proof of a classical result about projectivities between finite abelian groups. It is based on the concept of fundamental group lattice, studied in our previous papers \cite{8} and \cite{9}. A…
The main purpose of this paper is to provide a description of the fundamental group of a symplectic manifold in terms of Floer theoretic objects. As an application, we show that when counted with a suitable notion of multiplicity, non…
We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways…
This paper contains a complete proof of a fundamental theorem on the normalizers of unipotent subgroups in semisimple algebraic groups.
We construct examples of algebraic surfaces with interesting fundamental groups.
We introduce and analyse a general notion of fundamental group for noncommutative spaces, described by differential graded algebras. For this we consider connections on finitely generated projective bimodules over differential graded…
The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a $k$-algebra $A$, we consider the category of all connected gradings of $A$ by a group $G$ and we…
We define the algebraic fundamental group functor of a reductive group scheme over an arbitrary (non-empty) base scheme and prove that this functor is exact.
These lecture notes from a first course in algebraic topology use the fundamental group and orbit categories to classify covering spaces.
In this paper we show an index theorem for gerbes
For a class of affine algebraic groups $\mathcal C$ over a field, we define the notions of $\mathcal C$-fundamental gerbe of a fibered category, generalizing what we had done in arXiv:1204.1260 for finite group schemes. We give sufficient…
The Fundamental Theorem of Algebra can be thought of as a statement about the real numbers as a space, considered as an algebraic set over the real numbers as a field. This paper introduces what it means for an algebraic set or affine…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.