Related papers: What is a fundamental domain?
We determine the fundamental group of period domains over finite fields.
We exhibit an algorithm to compute a Dirichlet domain for a cofinite Fuchsian group Gamma. As a consequence, we compute the invariants of Gamma, including an explicit finite presentation for Gamma.
Fundamental domains are found for functions defined by general Dirichlet series and using basic properties of conformal mappings the Great Riemann Hypothesis is studied.
This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…
A semigroup $S$ is called an equational domain if any finite union of algebraic sets over $S$ is algebraic. For a finite simple semigroup we find necessary and sufficient conditions to be an equational domain. Moreover, we study semigroups…
We prove that a group has a DF domain if and only if has a Double Dirichlet domain. We give a good describtion of the side-paring transformation of such groups. In particular, those not fixing infinity have a common eigenvector. We also…
In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we…
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…
Classically domain theory is a rigourous mathematical structure to describe denotational semantics for programming languages and to study the computability of partial functions. Recently, the application of domain theory has also been…
We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…
The notion of maximal non valuative domain is introduced and characterized. An integral domain R is called a maximal non valuative domain if R is not a valuative domain but every proper overring of R is a valuative domain. Maximal non…
In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in $\mathbf{SL}_2(\mathbb{R})$ from which…
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.
In this paper, it is shown that a Fuchsian group, acting on the upper half-plane model for $\mathbb{H}^2$, admits a Ford domain which is also a Dirichlet domain, for some center, if and only if it is an index 2 subgroup of a reflection…
Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field, and let $\mathcal{C}_{H}$ be the corresponding cluster category. We give a description of the (standard) fundamental domain of $\mathcal{C}_{H} $ in the…
In this note we generalize Nori's definition of the fundamental group scheme from a rational point to an arbitrary base point so that when we take $X$ to be a field $k$ and the point to be $k\subseteq \bar{k}$ we still get a non trivial…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by…
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the…
We extend the definition of fundamental group scheme to non reduced schemes over any connected Dedekind scheme. Then we compare the fundamental group scheme of an affine scheme with that of its reduced part.