A topological realization of the congruence subgroup Kernel A

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly similar. We puzzled over this, in particular over the role of elementary matrices in both computations. We formulated a very general result on the fundamental group of a Satake compactification of a locally symmetric space. This lead to our joint paper [1] with Lizhen Ji and Les Saper on these fundamental groups. Although the results in it were intriguingly similar to the corresponding calculations of the congruence subgroup kernel of the underlying algebraic group in [5], we were not able to demonstrate a direct connection (cf. [1], ${\S}$7). The purpose of this note is to explain such a connection. A covering space is constructed from inverse limits of reductive Borel-Serre compactifications. The congruence subgroup kernel then appears as the group of deck transformations of this covering. The key to this is the computation of the fundamental group in [1]

Lp-cohomology of negatively curved manifolds

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds

Dynamics of Special Points on Intermediate Jacobians

We prove some general density statements about the subgroup of invertible points on intermediate jacobians; namely those points in the Abel-Jacobi image of nullhomologous algebraic cycles on projective algebraic manifolds.Comment: 10 page

Analysis of The Hipparcos Measurements of HD10697 - A Mass Determination of a Brown-Dwarf Secondary

HD10697 is a nearby main-sequence star around which a planet candidate has recently been discovered by means of radial-velocity measurements (Vogt et al. 1999, submitted to ApJ). The stellar orbit has a period of about three years, the secondary minimum mass is 6.35 Jupiter masses and the minimum semi-major axis is 0.36 milli-arc-sec (mas). Using the Hipparcos data of HD10697 together with the spectroscopic elements of Vogt et al. (1999) we found a semi-major axis of 2.1 +/- 0.7 mas, implying a mass of 38 +/- 13 Jupiter masses for the unseen companion. We therefore suggest that the secondary of HD10697 is probably a brown dwarf, orbiting around its parent star at a distance of 2 AU.Comment: 6 pages, 2 figures, LaTex, aastex, accepted for publication by ApJ Letter

Stability of the Higgs mass in theories with extra dimensions

We analyze the ultraviolet stability of the Higgs mass in recently proposed Kaluza-Klein models compactified on S_1/Z_2 or S_1/(Z_2\times Z_2'), both at the field theory and string theory level. Fayet-Iliopoulos terms of U(1) hypercharge are shown to be of vital importance for this discussion. Models with a single Higgs doublet seem to be generically affected by quadratic divergences.Comment: Contribution to the Proceedings of Durham IPPP meeting May 2001.(12 pages, LaTeX

Leo V: A Companion of a Companion of the Milky Way Galaxy

We report the discovery of a new Milky Way dwarf spheroidal galaxy in the constellation of Leo identified in data from the Sloan Digital Sky Survey. Leo V lies at a distance of about 180 kpc, and is separated by about 3 degrees from another recent discovery, Leo IV. We present follow-up imaging from the Isaac Newton Telescope and spectroscopy from the Hectochelle fiber spectrograph at the Multiple Mirror Telescope. Leo V's heliocentric velocity is 173.4 km/s, which is offset by about 40 km/s from that of Leo IV. A simple interpretation of the kinematic data is that both objects may lie on the same stream, though the implied orbit is only modestly eccentric (e = 0.2)Comment: Submitted to ApJ (Letters

Vacuum energy for the supersymmetric twisted D-brane in constant electromagnetic field

We calculate vacuum energy for twisted SUSY D-brane on toroidal background with constant magnetic or constant electric field. Its behaviour for toroidal D-brane (p=2) in constant electric field shows the presence of stable minimum for twisted versions of the theory. That indicates such a background maybe reasonable groundstate.Comment: LaTeX, 10 page

The SPLASH Survey: A Spectroscopic Analysis of the Metal-Poor, Low-Luminosity M31 dSph Satellite Andromeda X

Andromeda X (And X) is a newly discovered low-luminosity M31 dwarf spheroidal galaxy (dSph) found by Zucker et al. (2007) in the Sloan Digital Sky Survey (SDSS - York et al. 2000). In this paper, we present the first spectroscopic study of individual red giant branch stars in And X, as a part of the SPLASH Survey (Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo). Using the Keck II telescope and multiobject DEIMOS spectrograph, we target two spectroscopic masks over the face of the galaxy and measure radial velocities for ~100 stars with a median accuracy of sigma_v ~ 3 km/s. The velocity histogram for this field confirms three populations of stars along the sight line: foreground Milky Way dwarfs at small negative velocities, M31 halo red giants over a broad range of velocities, and a very cold velocity ``spike'' consisting of 22 stars belonging to And X with v_rad = -163.8 +/- 1.2 km/s. By carefully considering both the random and systematic velocity errors of these stars (e.g., through duplicate star measurements), we derive an intrinsic velocity dispersion of just sigma_v = 3.9 +/- 1.2 km/s for And X, which for its size, implies a minimum mass-to-light ratio of M/L =37^{+26}_{-19} assuming the mass traces the light. Based on the clean sample of member stars, we measure the median metallicity of And X to be [Fe/H] = -1.93 +/- 0.11, with a slight radial metallicity gradient. The dispersion in metallicity is large, sigma([Fe/H]) = 0.48, possibly hinting that the galaxy retained much of its chemical enrichment products. We discuss the potential for better understanding the formation and evolution mechanisms for M31's system of dSphs through (current) kinematic and chemical abundance studies, especially in relation to the Milky Way sample. (abridged version)Comment: Accepted for Publication in Astrophys. J. 14 pages including 7 figures and 2 tables (journal format