L^2-Betti numbers of one-relator groups

We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for all such groups G, the L^2-Betti numbers b_n^{(2)}(G) are 0 for all n>1. We also obtain some information about the L^2-cohomology of left-orderable groups, and deduce the non-L^2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.Comment: 18 pages, version 3, minor changes. To appear in Math. An

X-Ray and Radio Observations of Bright GeV Sources

We present X-ray and radio studies of sources which are brightabove 1 GeV (F_{>1GeV} > 4e-8 ph/cm^2/s. Only 11 out of ~30 of these gamma-ray sources have been identified with lower energy counterparts: 5 blazars and 6 pulsars. Three of these pulsars are surrounded by radio pulsar wind nebulae (PWN), two of which are also seen as bright, extended X-ray synchrotron nebulae. The ASCA X-ray telescope has observed 28 of the bright GeV sources, revealing an excess of F_{2-10keV} > 10e-12 ergs/cm^2/s sources within the {\it EGRET} error contours of the unidentified sources. Although several supernova remnants are positionally coincident with these sources, we find no X-ray evidence of high energy particle production in SNR shell shocks consistent with the GeV positions. We also present initial results from follow on radio imaging studies of several fields containing unidentified sources. We have discovered new X-ray/radio nebulae in three of these fields which are strong candidates for PWN. These sources, along with a similar nebula in CTA 1 and the PWN around PSR B1853+01 in W44, are all positionally coincident with variable EGRET sources. This suggests a class of variable gamma-ray sources associated with synchrotron emitting regions powered by the winds of young pulsars.Comment: 18 pages, 26 figures, To appear in the proceedings of the workshop: "The Nature of the Unidentified Galactic Gamma-Ray Sources" held at INAOE, Mexico, October 2000, (A.Carraminana, O. Reiner and D. Thompson,

Simulating rewetting events in intermittent rivers and ephemeral streams: A global analysis of leached nutrients and organic matter

Climate change and human pressures are changing the global distribution and the ex‐ tent of intermittent rivers and ephemeral streams (IRES), which comprise half of the global river network area. IRES are characterized by periods of flow cessation, during which channel substrates accumulate and undergo physico‐chemical changes (precon‐ ditioning), and periods of flow resumption, when these substrates are rewetted and release pulses of dissolved nutrients and organic matter (OM). However, there are no estimates of the amounts and quality of leached substances, nor is there information on the underlying environmental constraints operating at the global scale. We experi‐ mentally simulated, under standard laboratory conditions, rewetting of leaves, river‐ bed sediments, and epilithic biofilms collected during the dry phase across 205 IRES from five major climate zones. We determined the amounts and qualitative character‐ istics of the leached nutrients and OM, and estimated their areal fluxes from riverbeds. In addition, we evaluated the variance in leachate characteristics in relation to selected environmental variables and substrate characteristics. We found that sediments, due to their large quantities within riverbeds, contribute most to the overall flux of dis‐ solved substances during rewetting events (56%–98%), and that flux rates distinctly differ among climate zones. Dissolved organic carbon, phenolics, and nitrate contrib‐ uted most to the areal fluxes. The largest amounts of leached substances were found in the continental climate zone, coinciding with the lowest potential bioavailability of the leached OM. The opposite pattern was found in the arid zone. Environmental vari‐ ables expected to be modified under climate change (i.e. potential evapotranspiration, aridity, dry period duration, land use) were correlated with the amount of leached sub‐ stances, with the strongest relationship found for sediments. These results show that the role of IRES should be accounted for in global biogeochemical cycles, especially because prevalence of IRES will increase due to increasing severity of drying event

Heavy element production in a compact object merger observed by JWST

The mergers of binary compact objects such as neutron stars and black holes are of central interest to several areas of astrophysics, including as the progenitors of gamma-ray bursts (GRBs)1, sources of high-frequency gravitational waves (GW)2 and likely production sites for heavy element nucleosynthesis via rapid neutron capture (the r-process)3. Here we present observations of the exceptionally bright gamma-ray burst GRB 230307A. We show that GRB 230307A belongs to the class of long-duration gamma-ray bursts associated with compact object mergers4–6, and contains a kilonova similar to AT2017gfo, associated with the gravitational-wave merger GW1708177–12. We obtained James Webb Space Telescope mid-infrared (mid-IR) imaging and spectroscopy 29 and 61 days after the burst. The spectroscopy shows an emission line at 2.15 microns which we interpret as tellurium (atomic mass A=130), and a very red source, emitting most of its light in the mid-IR due to the production of lanthanides. These observations demonstrate that nucleosynthesis in GRBs can create r-process elements across a broad atomic mass range and play a central role in heavy element nucleosynthesis across the Universe