A pattern for torsion in Khovanov homology
We prove that certain specific sum of enhanced states produce torsion of order two in the Khovanov homology.
math.GT↗
arXiv subjects
R. Díaz
Publications and source records attributed to R. Díaz.
GLADE+: An Extended Galaxy Catalogue for Multimessenger Searches with Advanced Gravitational-wave Detectors
We present GLADE+, an extended version of the GLADE galaxy catalogue introduced in our previous paper for multimessenger searches with advanced gravitational-wave detectors. GLADE+ combines data from six separate but not independent astronomical catalogues: the GWGC, 2MPZ, 2MASS XSC, HyperLEDA, and WISExSCOSPZ galaxy catalogues, and the SDSS-DR16Q quasar catalogue. To allow corrections of CMB-frame redshifts for peculiar motions, we calculated peculiar velocities along with their standard deviations of all galaxies having $B$-band magnitude data within redshift $z=0.05$ using the "Bayesian Origin Reconstruction from Galaxies" formalism. GLADE+ is complete up to luminosity distance $d_L=47^{+4}_{-2}$ Mpc in terms of the total expected $B$-band luminosity of galaxies, and contains all of the brightest galaxies giving 90\% of the total $B$-band and $K$-band luminosity up to $d_L\simeq 130$ Mpc. We include estimations of stellar masses and individual binary neutron star merger rates for galaxies with $W1$ magnitudes. These parameters can help in ranking galaxies in a given gravitational wave localization volume in terms of their likelihood of being hosts, thereby possibly reducing the number of pointings and total integration time needed to find the electromagnetic counterpart.
astro-ph.CO↗
Brane gravity in 4D from Chern-Simons gravity theory
We evaluate a 5-dimensional Randall Sundrum type metric in the Lagrangian of the Einstein-Chern-Simons gravity, and then we derive an action and its corresponding field equations, for a 4-dimensional brane embedded in the 5-dimensional space-time of the theory, which in the limit l--0 leads to the 4-dimensional general relativity with cosmological constant. An interpretation of the h*a matter field present in the Einstein-Chern-Simons gravity action is given. As an application, we find some Friedmann-Lemaitre-Robertson-Walker cosmological solutions that exhibit accelerated behavior.
gr-qc↗
Pretzel knots up to nine crossings
There are infinitely many pretzel links with the same Alexander polynomial (actually with trivial Alexander polynomial). By contrast, in this note we revisit the Jones polynomial of pretzel links and prove that, given a natural number S, there is only a finite number of pretzel links whose Jones polynomials have span S. More concretely, we provide an algorithm useful for deciding whether or not a given knot is pretzel. As an application we identify all the pretzel knots up to nine crossings, proving in particular that $8_{12}$ is the first non-pretzel knot.
math.GT↗
Strategic Scientific Plan for Gemini Observatory
We present the Strategic Scientific Plan (SSP) for the direction and activities of the Gemini Observatory in the 2020s. The overarching goal is to ensure that Gemini best uses the available resources to serve the needs of its international user community throughout the coming decade. The actionable items fall into three general categories: (1) preserving Gemini's current facilities and strengths; (2) developing instrumentation and software systems, including data pipelines, to enable new scientific capabilities that build on those strengths; (3) strategizing how visiting instruments can deliver additional valuable capabilities. We provide a high-level timeline (schematically illustrated in one figure) for the main developments discussed in this SSP. The schedule is ambitious, but in light of the recent Gemini in the Era of Multi-Messenger Astronomy (GEMMA) award from the NSF, the plan becomes achievable. Lists of milestones are given for gauging progress. As these milestones are reached and new instruments become available, some current instruments will need to be retired; we make recommendations in this regard. The final section concludes by reemphasizing the importance of a strong partnership committed to the needs of all members.
astro-ph.IM↗