arXiv subjects
Publications and source records attributed to James Morgan.
Milnor computed the volumes of ideal hyperbolic prisms as part of an effort to construct 3-manifolds whose volumes are finite rational sums of the Lobachevsky function evaluated at rational multiples of pi. Motivated by these results and with an eye to related applications, we prove a volume formula for arbitrary ideal hyperbolic antiprisms, also called drums.
We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string braid construction. For the 2-bridge links satisfying this condition we construct explicit angle structures on the Sakuma-Weeks triangulations and compute both multiplicative and additive lower bounds on the complexity of the link complements via volume estimates. These lower bounds are an improvement on existing volume estimates for the 2-bridge links examined.
Following work of Jaco and Rubinstein (2006), which (non-constructively) proved that any 3-manifold admits a one-vertex layered triangulation, we present an algorithm, with implementation using Regina, that uses a combinatorial presentation of a Heegaard diagram to construct a generalised notion of a layered triangulation. We show that work of Husz\'ar and Spreer (2019) extends to our construction: given a genus-$g$ Heegaard splitting, our algorithm generates a triangulation with cutwidth bounded above by $4g-2$. Beyond Heegaard splittings, our construction actually extends to a natural generalisation of Dehn fillings: given a one-vertex triangulation with a genus-$g$ boundary component $B$, we can construct a one-vertex triangulation of any 3-manifold obtained by filling $B$ with a handlebody. To demonstrate the usefulness of our algorithm, we present findings from preliminary computer searches using this algorithm.
The Extended Persistent Homology Transform (XPHT) is a topological transform which takes as input a shape embedded in Euclidean space, and to each unit vector assigns the extended persistence module of the height function over that shape with respect to that direction. We can define a distance between two shapes by integrating over the sphere the distance between their respective extended persistence modules. By using extended persistence we get finite distances between shapes even when they have different Betti numbers. We use Morse theory to show that the extended persistence of a height function over a manifold with boundary can be deduced from the extended persistence for that height function restricted to the boundary, alongside labels on the critical points as positive or negative critical. We study the application of the XPHT to binary images; outlining an algorithm for efficient calculation of the XPHT exploiting relationships between the PHT of the boundary curves to the extended persistence of the foreground.
The Arcanum mission is a proposed L-class spacecraft that highlights the revolutionary approach which can now be taken to future space mission design. Using the case of the SpaceX Starship vehicle and in particular the high mass and volume characteristics of this launcher, the feasible large size of future missions, even with high delta-V transfer requirements, are analysed. A demonstrator vehicle, designed to support a large and capable science platform with multiple components, is detailed, clearly showing the range and depth of science goals that will be answerable thanks to the current revolution in super heavy-lift launch vehicles.
A coming resurgence of super heavy-lift launch vehicles has precipitated an immense interest in the future of crewed spaceflight and even future colonisation efforts. While it is true that a bright future awaits this sector, driven by commercial ventures and the reignited interest of old space-faring nations, and the joining of new ones, little of this attention has been reserved for the science-centric applications of these launchers. The Arcanum mission is a proposal to use these vehicles to deliver an L-class observatory into a highly eccentric orbit around Neptune, with a wide-ranging suite of science goals and instrumentation tackling Solar System science, planetary science, Kuiper Belt Objects and exoplanet systems.
This is a decentralized position paper on crypto art, which includes viewpoints from different actors of the system: artists, collectors, galleries, art scholars, data scientists. The writing process went as follows: a general definition of the topic was put forward by two of the authors (Franceschet and Colavizza), and used as reference to ask to a set of diverse authors to contribute with their viewpoints asynchronously and independently. No guidelines were offered before the first draft, if not to reach a minimum of words to justify a separate section/contribution. Afterwards, all authors read and commented on each other's work and minimal editing was done. Every author was asked to suggest open questions and future perspectives on the topic of crypto art from their vantage point, while keeping full control of their own sections at all times. While this process does not necessarily guarantee the uniformity expected from, say, a research article, it allows for multiple voices to emerge and provide for a contribution on a common topic. The ending section offers an attempt to pull all these threads together into a perspective on the future of crypto art.