arXiv subjects

S. Hernández

Publications and source records attributed to S. Hernández.

8 recordsLinked to original sources

arXiv2025

Bohr compactification and Chu duality of non-abelian locally compact groups

The \emph{Bohr compactification} of an arbitrary topological group $G$ is defined as the group compactification $(bG,b)$ with the following universal property: for every continuous homomorphism $h$ from $G$ into a compact group $K$ there is a continuous homomorphism $h^{b}$ from $bG$ into $K$ extending $h$ in the sense that $h=h^b \circ b$. The Bohr compactification $(bG,b)$ is the unique (up to equivalence) largest compactification of $G$. Although, for locally compact Abelian groups, the Bohr compactification is a big monster, for non-Abelian groups the situation is much more interesting and it can be said that all options are possible. Here we are interested in locally compact groups whose Bohr compactification is \emph{small}. Among other results, we characterize when the Bohr the Bohr compactification of a locally compact group is topologically isomorphic to its Chu or unitary quasi-dual. Our results fixe some incorrect statements appeared in the literature.

math.GR↗

arXiv2024

The Baire property and precompact duality

We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Domínguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au$β$enhofer and Dikranjan.}

math.GR↗

arXiv2023

The High-Altitude Water Cherenkov (HAWC) Observatory in México: The Primary Detector

The High-Altitude Water Cherenkov (HAWC) observatory is a second-generation continuously operated, wide field-of-view, TeV gamma-ray observatory. The HAWC observatory and its analysis techniques build on experience of the Milagro experiment in using ground-based water Cherenkov detectors for gamma-ray astronomy. HAWC is located on the Sierra Negra volcano in México at an elevation of 4100 meters above sea level. The completed HAWC observatory principal detector (HAWC) consists of 300 closely spaced water Cherenkov detectors, each equipped with four photomultiplier tubes to provide timing and charge information to reconstruct the extensive air shower energy and arrival direction. The HAWC observatory has been optimized to observe transient and steady emission from sources of gamma rays within an energy range from several hundred GeV to several hundred TeV. However, most of the air showers detected are initiated by cosmic rays, allowing studies of cosmic rays also to be performed. This paper describes the characteristics of the HAWC main array and its hardware.

astro-ph.HE↗

arXiv2020

A survey of active galaxies at TeV photon energies with the HAWC gamma-ray observatory

The High Altitude Water Cherenkov Gamma-Ray Observatory (HAWC) continuously detects TeV photons and particles within its large field-of-view, accumulating every day a deeper exposure of two thirds of the sky. We analyzed 1523~days of HAWC live data acquired over four and a half years, in a follow-up analysis of {138} nearby ($z<0.3$) active galactic nuclei from the {\em Fermi} 3FHL catalog culminating within $40^\circ$ of the zenith at Sierra Negra, the HAWC site. This search for persistent TeV emission used a maximum-likelihood analysis assuming intrinsic power-law spectra attenuated by pair production of gamma-ray photons with the extragalactic background light. HAWC clearly detects persistent emission from Mkn~421 and Mkn~501, the two brightest blazars in the TeV sky, at 65$σ$ and 17$σ$ level, respectively. {Weaker evidence for long-term emission is found for three other known very-high energy emitters:} the radiogalaxy M87 and the BL Lac objects VER~J0521+211 and 1ES~1215+303, the later two at $z\sim 0.1$. We find evidence for collective emission from the set of 30 previously reported very high-energy sources that excludes Mkn~421 and Mkn~501 with a random probability $\sim 10^{-5}$. Upper limits are presented for the sample under the power-law assumption and in the predefined (0.5-2.0), (2.0-8.0) and (8.0-32.0) TeV energy intervals.

astro-ph.HE↗

arXiv2019

On convergent sequences in dual groups

We provide some characterizations of precompact abelian groups $G$ whose dual group $G_p^\wedge$ endowed with the pointwise convergence topology on elements of $G$ contains a nontrivial convergent sequence. In the special case of precompact abelian \emph{torsion} groups $G$, we characterize the existence of a nontrivial convergent sequence in $G_p^\wedge$ by the following property of $G$: \emph{No infinite quotient group of $G$ is countable.} Finally, we present an example of a dense subgroup $G$ of the compact metrizable group $\mathbb{Z}(2)^ω$ such that $G$ is of the first category in itself, has measure zero, but the dual group $G_p^\wedge$ does not contain infinite compact subsets. This complements Theorem 1.6 in [J.E.~Hart and K.~Kunen, Limits in function spaces and compact groups, \textit{Topol. Appl.} \textbf{151} (2005), 157--168]. As a consequence, we obtain an example of a precompact reflexive abelian group which is of the first Baire category.

math.GN↗

arXiv2017

Extended gamma-ray sources around pulsars constrain the origin of the positron flux at Earth

The unexpectedly high flux of cosmic ray positrons detected at Earth may originate from nearby astrophysical sources, dark matter, or unknown processes of cosmic-ray secondary production. We report the detection, using the HighAltitude Water Cherenkov Observatory (HAWC), of extended tera-electron volt gamma-ray emission coincident with the locations of two nearby middle-aged pulsars (Geminga and PSR B0656+14). The HAWC observations demonstrate that these pulsars are indeed local sources of accelerated leptons, but the measured tera-electron volt emission profile constrains the diffusion of particles away from these sources to be much slower than previously assumed. We demonstrate that the leptons emitted by these objects are therefore unlikely to be the origin of the excess positrons, which may have a more exotic origin.

astro-ph.HE↗

arXiv2012

Precompact groups and property (T)

For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete, and we investigate to what extent this remains true for precompact groups, i.e. for dense subgroups of compact groups. We find that: (a) if $G$ is a metrizable precompact group, then $\hat G$ is discrete; (b) if $G$ is a countable non-metrizable precompact group, then $\hat G$ is not discrete; (c) every non-metrizable compact group contains a dense subgroup $G$ for which $\hat G$ is not discrete. This generalizes to the non-Abelian case what was known for Abelian groups. Kazhdan's property (T) can be defined in similar terms, but we must consider representations without non-zero invariant vectors rather than irreducible representations. If $G$ is any countable Abelian precompact group, then $G$ does not have property (T), although $\hat G$ is discrete if $G$ is metrizable.

math.GN↗

arXiv2012

The dual space of precompact groups

For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete. In an earlier paper we proved that $\hat G$ is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when $G$ is an almost metrizable precompact group.

math.RT↗