Weak Riemannian manifolds from finite index subfactors

Let $N\subset M$ be a finite Jones' index inclusion of II$_1$ factors, and denote by $U_N\subset U_M$ their unitary groups. In this paper we study the homogeneous space $U_M/U_N$, which is a (infinite dimensional) differentiable manifold, diffeomorphic to the orbit $${\cal O}(p) =\{u p u^*: u\in U_M\}$$ of the Jones projection $p$ of the inclusion. We endow ${\cal O}(p)$ with a Riemannian metric, by means of the trace on each tangent space. These are pre-Hilbert spaces (the tangent spaces are not complete), therefore ${\cal O}(p)$ is a weak Riemannian manifold. We show that ${\cal O}(p)$ enjoys certain properties similar to classic Hilbert-Riemann manifolds. Among them, metric completeness of the geodesic distance, uniqueness of geodesics of the Levi-Civita connection as minimal curves, and partial results on the existence of minimal geodesics. For instance, around each point $p_1$ of ${\cal O}(p)$, there is a ball $\{q\in {\cal O}(p):\|q-p_1\|<r\}$ (of uniform radius $r$) of the usual norm of $M$, such that any point $p_2$ in the ball is joined to $p_1$ by a unique geodesic, which is shorter than any other piecewise smooth curve lying inside this ball. We also give an intrinsic (algebraic) characterization of the directions of degeneracy of the submanifold inclusion ${\cal O}(p)\subset {\cal P}(M_1)$, where the last set denotes the Grassmann manifold of the von Neumann algebra generated by $M$ and $p$.Comment: 19 page

Projective spaces of a C*-algebra

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invertible group of A. Moreover, several metrics (chordal, spherical, pseudo-chordal, non-Euclidean - in Schwarz-Zaks terminology) are considered, allowing a comparison among P(p), the Grassmann manifold of A and the space of positive elements which are unitary with respect to the bilinear form induced by the reflection e = 2p-1. Among several metrical results, we prove that geodesics are unique and of minimal length when measured with the spherical and non-Euclidean metrics.Comment: 26 pages, Late

Geometry of oblique projections

Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P_a determined by the different involutions #_a induced by positive invertible elements a in A. The maps f_p: P \to P_a sending p to the unique q in P_a with the same range as p and \Omega_a: P_a \to P sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q, r in A with |q-r|<1 such that there exists a positive element a in A verifying that q, r are in P_a. In this case q and r can be joined by an unique short geodesic along the space of idempotents Q of A.Comment: 25 pages, Latex, to appear in Studia Mathematic

Polarization and photometric observations of the gamma-ray blazar PG 1553+113

We present the results of an observational photo-polarimetry campaign of the blazar PG 1553+113 at optical wavelengths. The blazar was recently detected at very high energies (> 100 GeV) by the H.E.S.S and MAGIC gamma-ray Cherenkov telescopes. Our high-temporal resolution data show significant variations in the linear polarization percentage and position angle at inter-night time-scales, while at shorter (intra-night) time-scales both parameters varied less significantly, if at all. Changes in the polarization angle seem to be common in gamma-ray emitting blazars. Simultaneous differential photometry (through the B and R bands) shows no significant variability in the total optical flux. We provide B and R magnitudes, along with a finding chart, for a set of field stars suitable for differential photometry.Comment: 4 pages, 3 figures. To be published by Astronomy and Astrophysic

Minimal hermitian matrices with fixed entries outside the diagonal

We survey some results concerning the problem of finding the complex hermitian matrix or matrices of least supremum norm with variable diagonal. Some qualitative general results are given and more specific descriptions are shown for the 3 x 3 case. We also comment some results and examples concerning this approximation problem.Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Mata Lorenzo, Luis E.. Universidad Simón Bolívar; VenezuelaFil: Mendoza, Alberto.. Universidad Simón Bolívar; VenezuelaFil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simón Bolívar; VenezuelaFil: Varela, Alejandro. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

Gamma Ray Bursts with peculiar temporal asymmetry

Based on the study of temporal asymmetry of 631 gamma ray bursts from the BATSE 3B catalog by Link and Epstein [Ap J 466, 764 (1996)], we identify the population of bursts whose rising times are longer than their decays, thus showing atypical profiles. We analyse their sky distribution, morphology, time-space clustering and other average properties and compare them with those associated with the bulk of the bursts. We show how most of the peculiar bursts analysed are consistent with recent fireball models, but a fraction of bursts ($\sim 4$% of the total sample) appear to be inconsistent.Comment: mn style (included in the submission), 4 figures that must be printed separately. Submitted to Monthly Notices of RA

Looking for blazars in a sample of unidentified high-energy emitting Fermi sources

Context. Based on their overwhelming dominance among associated Fermi γ-ray catalogue sources, it is expected that a large fraction of the unidentified Fermi objects are blazars. Through crossmatching between the positions of unidentified γ-ray sources from the First Fermi Catalog of γ-ray sources emitting above 10 GeV (1FHL) and the ROSAT and Swift/XRT catalogues of X-ray objects and between pointed XRT observations, a sample of 36 potential associations was found in previous works with less than 15 arcsec of positional offset. One-third of them have recently been classified; the remainder, though believed to belong to the blazar class, still lack spectroscopic classifications. Aims. We study the optical spectrum of the putative counterparts of these unidentified gamma-ray sources in order to find their redshifts and to determine their nature and main spectral characteristics. Methods. An observational campaign was carried out on the putative counterparts of 13 1FHL sources using medium-resolution optical spectroscopy from the Osservatorio Astronomico di Bologna in Loiano, Italy; the Telescopio Nazionale Galileo and the Nordic Optical Telescope, both in the Canary Islands, Spain; and the Observatorio Astronómico Nacional San Pedro Mártir in Baja California, Mexico. Results. We were able to classify 14 new objects based on their continuum shapes and spectral features. Conclusions. Twelve new blazars were found, along with one new quasar and one new narrow line Seyfert 1 (NLS1) to be potentially associated with the 1FHL sources of our sample. Redshifts or lower limits were obtained when possible alongside central black hole mass and luminosity estimates for the NLS1 and the quasar.Fil: Marchesini, Ezequiel Joaquín. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Masetti, Nicola. Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna; ItaliaFil: Chavushyan, V.. Instituto Nacional de Astrofísica, Óptica y Electrónica; MéxicoFil: Cellone, Sergio Aldo. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Andruchow, Ileana. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Bassani, L.. Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna; ItaliaFil: Bazzano, A.. Istituto di Astrofisica e Planetologia Spaziali; ItaliaFil: Jiménez-Bailón, E.. Universidad Nacional Autónoma de México; MéxicoFil: Landi, R.. Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna; ItaliaFil: Malizia, A.. Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna; ItaliaFil: Palazzi, E.. Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna; ItaliaFil: Patiño Álvarez, V.. Instituto Nacional de Astrofísica, Óptica y Electrónica; MéxicoFil: Rodríguez Castillo, G. A.. Osservatorio Astronomico di Roma; ItaliaFil: Stephen, J. B.. Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna; ItaliaFil: Ubertini, P.. Istituto di Astrofisica e Planetologia Spaziali; Itali

In search for natural wormholes

We have investigated 631 time profiles of gamma ray bursts from the BATSE database searching for observable signatures produced by microlensing events related to natural wormholes. The results of this first search of topologically nontrivial objects in the Universe can be used to constrain their number and mass.Comment: Mod. Phys. Lett. A. (in press) Latex (revtex style) with no figure