With the exception of gravitation, the known fundamental interactions of Nature are mediated by gauge fields. A comparison of the candidate groups for a gauge theory possibly describing gravitation favours the Poincaré group as the obvious choice. This theory gives Einstein’s equations in a particular case, and Newton’s law in the static non-relativistic limit, being seemingly sound at the clas...

The Fluid Flow Group (FFG) at NESTmaintains flow standards to perform calibrations of gas flowmeters over the 3.7x 10-2L/rein@to 78,000 L/rein flow range. Uncertainty analyses based on the propagation of uncertainties method show that the uncertainties of the provers range from O.16’%o to O.19’?40. The results of inter-laboratory comparisons and intra-laboratory comparisons (i.e., “crossover te...

We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group Γ with cofinite area. As a consequence, we compute the invariants of Γ, including an explicit finite presentation for Γ. Let Γ ⊂ PSL2(R) be a Fuchsian group, a discrete group of orientationpreserving isometries of the upper half-plane H with hyperbolic metric d. A fundamental domain for Γ is a closed domain D ⊂ H such th...

In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

It had been unclear how to define the topological charge in the reduced model which is given by a zero-volume limit of lattice gauge theory. In ref. [1], the authors proposed to define the topological charge in a “fermionic way” by using the overlap Dirac operator and showed that there actually exist non-trivial topological sectors. In ref. [2], a general expression of the topological charge wa...

In Lecture 4, we learned about an algebraic method for describing and classifying structures. In this lecture, we look at using algebra to find combinatorial descriptions of topological spaces. We begin by looking at an equivalence relation called homotopy that gives a classification of spaces that is coarser that homeomorphism, but respects the finer classification. That is, two spaces that ha...

Suppose the finite group G acts as orientation preserving homeomorphisms of the oriented surface S of genus g . This determines an irreducible subvariety Jtg of the moduli space J?g of Riemann surfaces of genus g consisting of all surfaces with a group Gx of holomorphic homeomorphisms of the same topological type as G. This family is determined by an equivalence class of epimorphisms <// from a...

Let K be a totally real algebraic number field and O an order in a quaternion algebra A over K. Assume that the group O1 of units in O with reduced norm equal to 1 is embedded into PSL2(R) as an arithmetic Fuchsian group. It is shown how Ford’s algorithm can be effectively applied in order to determine a fundamental domain of O1 as well as a complete system of generators of O1.

In Lecture 4, we learned about an algebraic method for describing and classifying structures. In this lecture, we look at using algebra to find combinatorial descriptions of topological spaces. We begin by looking at an equivalence relation called homotopy that gives a classification of spaces that is coarser that homeomorphism, but respects the finer classification. That is, two spaces that ha...