We construct new manifolds with SU(3) holonomy that are candidate vacua for superstring theory and give a detailed explanation of the techniques involved. Some of these manifolds have a non-abelian fundamental group and thus can lead to a rank five low energy gauge group. Models with an odd number of generations are obtained. ^Θ* violation is discussed in this context and shown to occur generic...

We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of Bohmian mechanics, a quantum theory without observers from which the quantum formalism can be derived. What we do can be regarded as generalizing the Bohmian d...

In this paper we tackle the problem of constructing explicit examples of topological cocycles of Roberts’ net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some crucial results of the algebraic framework of quantization, we address the problem of the constructi...

The goal of this paper is to explore basic topics in Algebraic Topology. The paper will first begin by exploring the concept of loops on topological spaces and how one can look at these loops and form a group. From there, it moves to discuss covering spaces giving basic definitions and constructing the universal cover. After establishing this, covering spaces are used to calculate the fundament...

The conventional topological description given by the fundamental group of nematic order parameter does not adequately explain the entangled defect line structures that have been observed in nematic colloids. We introduce a new topological invariant, the self-linking number, that enables a complete classification of entangled defect line structures in general nematics, even without particles, a...