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Blair, Campisi, Taylor, and Tomova introduced a non-negative integer-valued invariant L ( S ) of a smooth surface S in the 4-sphere. In this paper, we extend previous work done by the authors with Scott Taylor to compute the invariant L ( S ) of a knotted surface in 4-space. We further explore the combinatorics of pants decompositions to give sharp bounds for the L -invariant of large families of bridge trisections. As an application, we show that surfaces with L ( S ) ≤ 2 must be unknotted.

In 2018, M. Chu and S. Tillmann gave a lower bound for the trisection genus of a closed 4-manifold in terms of the Euler characteristic of MM and the rank of its fundamental group. We show that given a group GG, there exists a 4-manifold MM with fundamental group GG with trisection genus achieving Chu-Tillmann’s lower bound.

At the time of this meeting, the latest Gaia data release is EDR3, published on 3 December 2020, but the next one, DR3, will appear soon, on 13 June 2022. This contribution describes, on the one hand, Gaia EDR3 results on massive stars and young stellar clusters, placing special emphasis on how a correct treatment of the astrometric and photometric calibration yields results that are simultaneously precise and accurate. On the other hand, it gives a brief description of the exciting results we can expect from Gaia DR3.

•Aqueous solutions of TNT and RDX quantified over time using GC/NCI-MS.•Degradation occurs independent of solution salinity.•UV light exposure rapidly increases rate of decomposition.•Bicyclic degradation products of TNT identified by ESI-MS. Terrorist attacks in a maritime setting, such as the bombing of the USS Cole in 2000, or the detection of underwater mines, require the development of proper protocols to collect and analyse explosive material from a marine environment. In addition to proper analysis of the explosive material, protocols must also consider the exposure of the material to potentially deleterious elements, such as UV light and salinity, time spent in the environment, and time between storage and analysis. To understand how traditional explosives would be affected by such conditions, saline solutions of explosives were exposed to natural and artificial sunlight. Degradation of the explosives over time was then quantified using negative chemical ionization gas chromatography mass spectrometry (GC/NCI-MS). Two explosives, trinitrotoluene (TNT) and cyclotrimethylenetrinitramine (RDX), were exposed to different aqueous environments and light exposures with salinities ranging from freshwater to twice the salinity of ocean water. Solutions were then aged for up to 6 months to simulate different conditions the explosives may be recovered from. Salinity was found to have a negligible impact on the degradation of both RDX and TNT. RDX was stable in solutions of all salinities while TNT solutions degraded regardless of salinity. Solutions of varying salinities were also exposed to UV light, where accelerated degradation was seen for both explosives. Potential degradation products of TNT were identified using electrospray ionization mass spectrometry (ESI-MS), and correspond to proposed degradation products discussed in previously published works [1].

Urea nitrate (UN) is an improvised explosive made from readily available materials. The carbon and nitrogen isotope composition of UN and its component ions, urea and nitrate, could aid in a forensic investigation. A method was developed to separate UN into its component ions for δ 15N measurements by dissolving the sample with KOH, drying the sample, followed by removal of the urea by dissolution into 100% methanol. UN was synthesized to assess for preservation of the carbon and nitrogen isotope compositions of reactants (urea and nitric acid) and product UN. Based on nitrogen isotope mass balance, all UN samples contained varying amounts of excess nitric acid, making the ionic separation an essential step in the nitrogen isotope analysis. During UN synthesis experiments, isotopic composition of the reactants is preserved in the product UN, but the urea in the product UN is slightly enriched in 15N (<1‰) relative to the reactant urea. Published isotopic compositions of UN reactants, urea and nitric acid, have large ranges (urea δ 15N = −10.8 to +3.3‰; urea δ 13C = −18.2 to −50.6‰; and nitric acid δ 15N = −1.8 to +4.0‰). The preservation of isotopic composition of reactants in UN, along with a significant variability in isotopic composition of reactants, indicates that isotope ratio analysis may be used to test if urea or nitric acid collected during an investigation is a possible reactant for a specific UN sample. The carbon and nitrogen isotope ratios differ significantly between two field-collected UN samples, as well as the lab-synthesized UN samples. These observed variations suggest that this approach is useful for discriminating between materials which are otherwise chemically identical.

Hot dust-obscured galaxies (Hot DOGs), the most infrared (IR) luminous objects selected by the WISE all-sky mid-IR survey, have yielded a sample of intrinsically luminous quasars (QSOs) with obscured nuclear activity and hot dust temperatures. The molecular gas excitation properties have yet to be examined in detail under such extreme conditions. Here we study the most far-IR luminous \\textit{WISE} Hot DOG W2246-0526, focusing on ALMA observations of the central host galaxy. Multi-J CO transition measurements at J=2-1, 5-4, 7-6, 12-11, and 17-16 provide the first self-consistent modeling constraints on the molecular gas and dust properties of any WISE Hot DOG to date, providing a benchmark for future studies of dust-obscured QSOs. We implement a state-of-the-art TUrbulent Non-Equilibrium Radiative transfer model (TUNER) that simultaneously models both the line and dust continuum measurements. The extreme CO spectral line energy distribution seems to turnover around the CO(12-11) transition, likely making this among the most highly excited galaxies ever reported. The model infers a molecular gas mass \\(\\sim 8\\times10^{10}\\)\\,\\Msun, and we conclude that J\\(\\ge\\)3 CO line luminosities trace the bulk of the molecular gas mass for this extreme system unlike low-excitation conditions calibrated locally. W2246-0526 is a rapidly evolving system, with a high mean value of the molecular gas kinetic temperature versus dust temperature \\(T_\\mathrm{k}\\) / \\(T_\\mathrm{d} \\sim 4.3\\). This may be due to the shocks and outflows injecting kinetic energy within the central kpc of this host that have previously been reported. These signs of highly excited molecular gas in W2246-0526 motivates obtaining well-sampled CO ladders in larger samples to better understand the conditions within these short-lived episodes associated with the most obscured supermassive black hole activity.

We present observations of mid-J J=4-3 or J=5-4 carbon monoxide (CO) emission lines and continuum emission from a sample of ten of the most luminous log(L/L_solar)~14 Hot Dust-Obscured Galaxies (Hot DOGs) discovered by the Wide-field Infrared Survey Explorer (WISE) with redshifts up to 4.6. We uncover broad spectral lines (FWHM~400 km/s) in these objects, suggesting a turbulent molecular interstellar medium (ISM) may be ubiquitous in Hot DOGs. A halo of molecular gas, extending out to a radius of 5 kpc is observed in W2305-0039, likely supplied by 940 km/s molecular outflows. W0831+0140 is plausibly the host of a merger between at least two galaxies, consistent with observations made using ionized gas. These CO(4-3) observations contrast with previous CO(1-0) studies of the same sources: the CO(4-3) to CO(1-0) luminosity ratios exceed 300 in each source, suggesting that the lowest excited states of CO are underluminous. These findings show that the molecular gas in Hot DOGs is consistently turbulent, plausibly a consequence of AGN feedback, triggered by galactic mergers.

Motivated by M. Scharlemann and A. Thompson's definition of thin position of 3-manifolds, we define the width of a handle decomposition a 4-manifold and introduce the notion of thin position of a compact smooth 4-manifold. We determine all manifolds having width equal to \\(\\{1,\\dots, 1\\}\\), and give a relation between the width of \\(M\\) and its double \\(M\\cup_{id_\\partial} \\overline M\\). In particular, we describe how to obtain genus \\(2g+2\\) and \\(g+2\\) trisection diagrams for sphere bundles over orientable and non-orientable surfaces of genus \\(g\\), respectively. By last, we study the problem of describing relative handlebodies as cyclic covers of 4-space branched along knotted surfaces from the width perspective.

Bridge multisections are combinatorial descriptions of surface links in 4-space using tuples of trivial tangles. They were introduced by Islambouli, Karimi, Lambert-Cole, and Meier to study curves in rational surfaces. In this paper, we prove a uniqueness result for bridge multisections of surfaces in 4-space: we give a complete set of moves relating to any two multiplane diagrams of the same surface. This is done by developing a surgery operation on multiplane diagrams called band surgery. Another application of this surgery move is that any \\(n\\)-valent graph with an \\(n\\)-edge coloring is the spine of a bridge multisection for an unknotted surface. We also prove that any multisected surface in \\(S^4\\) can be unknotted by finitely many band surgeries.

Heegaard splittings stratify 3-manifolds by complexity; only \\(S^3\\) admits a genus-zero splitting, and only \\(S^3\\), \\(S^1 \\times S^2\\), and lens spaces \\(L(p,q)\\) admit genus-one splittings. In dimension four, the second author and Jeffrey Meier proved that only a handful of simply-connected 4-manifolds have trisection genus two or less, while Meier conjectured that if \\(X\\) admits a genus-three trisection, then \\(X\\) is diffeomorphic to a spun lens space \\(S_p\\) or its sibling \\(S_p'\\), \\(S^4\\), or a connected sum of copies of \\(\\pm \\mathbb{CP}^2\\), \\(S^1 \\times S^3\\), and \\(S^2 \\times S^2\\). We prove Meier's conjecture in the case that \\(X\\) admits a weakly reducible genus-three trisection, where weak reducibility is a new idea adapted from Heegaard theory and is defined in terms of disjoint curves bounding compressing disks in various handlebodies. The tools and techniques used to prove the main theorem borrow heavily from 3-manifold topology. Of independent interest, we give a trisection-diagrammatic description of 4-manifolds obtained by surgery on loops and spheres in other 4-manifolds.