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In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of R4. After an overview of the technique, we will present two specific examples, discuss the associated matter models by solving the Einstein equations, and determine the physical viability by examining the energy conditions. We compare the resulting model directly with existing models of matter distributions in extragalactic systems, to highlight the viability of utilizing exotic smooth structures to understand the existence and distribution of dark matter.

This work presents an approach to track the spacetime topology in casual dynamical triangulations. The focus will be on a basic demonstration of the validity of the model through simulations in dimension 1+1. We will evaluate this model using standard tools, such as the spectral dimension, and will also present a calculation of the expectation value of a topological invariant, the Euler Characteristic. We will also briefly mention the recently completed dimension 3 case, in which we implemented an algorithm to find the fundamental group in this framework.

In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in dimension 3, and a complete set of the topological spaces branched over several graphs are found. We also include some new visualizations of the branched covering construction, in order to aid and clarify the understanding of how these structures can be used in quantum gravity to realize the topological nature of the spacetime foam.

In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of \\(\\mathbb{R}^4\\). We will present three distinct examples, discuss their associated matter models by solving the Einstein equations, and determine their physical viability by examining the energy conditions. We will also compare one of the models directly with existing models of matter distributions in extragalactic systems, to highlight the viability of utilizing exotic smooth structures to understand the existence and distribution of dark matter.

In this paper we will discuss how cosmic strings can be used to bridge the gap between the local geometry of our spacetime model and the global topology. The primary tool is the theory of foliations and surfaces, and together with observational constraints we can isolate several possibilities for the topology of the spatial section. This implies that the discovery of cosmic strings would not just be significant for an understanding of structure formation in the early universe, but also for the global properties of the spacetime model.

We present and evaluate the Merrimack College Mobile Lightboard, which we built in 2017 and which is still in use in 2025. Our design was closely based on that of the groundbreaking 2014 Duke University Lightboard but with a smaller glass pane, 5 feet wide instead of 6 feet wide. The resulting scaled-down board is small enough to move in and out of individual faculty offices, but large enough to make detailed videos. An updated construction cost estimate is provided, and recent upgrades are briefly discussed. We believe that personalized office-based lightboarding represents an attractive option for many faculty members, with strengths that complement those of centralized installations. Our successful build suggests that this option is technically and financially feasible at many if not most higher education institutions.

In this paper we describe an approach to construct semiclassical partition functions in gravity which are complete in the sense that they contain a complete description of the differentiable structures of the underlying 4-manifold. In addition, we find our construction naturally includes cosmic strings. We discuss some possible applications of the partition functions in the fields of both quantum gravity and topological string theory

We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert space of cylindrical functions. We will also discuss the area and Hamiltonian operators, and show how they depend on the topology. This extends the idea of \"background independence\" in loop quantum gravity to include topology as well as geometry. It is hoped this work will confirm the usefulness of the topspin network formalism and open up several new avenues for research into quantum gravity.

In this paper we calculate the effect of the inclusion of exotic smooth structures on typical observables in Euclidean quantum gravity. We do this in the semiclassical regime for several gravitational free-field actions and find that the results are similar, independent of the particular action that is chosen. These are the first results of their kind in dimension four, which we extend to include one-loop contributions as well. We find these topological features can have physically significant results without the need for additional exotic physics.

We present an algorithm which determines the fundamental group of a spatial section using topspin networks. Tracking the topology of the spatial section is a unique feature of this approach, which is not possible in standard Loop Quantum Gravity. This leads to an example of spatial topology change in a smooth 4-manifold represented by a topspin foam.