Universal covers and 3-manifolds

AbstractIn this paper, we show that if a finitely presented group G is the fundamental group of a finite fake surface in which the link of any vertex is not homeomorphic to the 1-skeleton of a tetrahedron, then there is a finite 2-complex K with π1(K)≅G and whose universal cover K̃ has the proper homotopy type of a 3-manifold. As a consequence, the cohomology group H2(G;ZG) is free abelian

SHALOS: Statistical Herschel-ATLAS lensed objects selection

Context. The statistical analysis of large sample of strong lensing events can be a powerful tool to extract astrophysical or cosmological valuable information. Their selection using submillimetre galaxies has been demonstrated to be very effective with more than ∼200 proposed candidates in the case of Herschel-ATLAS data and several tens in the case of the South Pole Telescope. However, the number of confirmed events is still relatively low, i.e. a few tens, mostly because of the lengthy observational validation process on individual events. Aims. In this work we propose a new methodology with a statistical selection approach to increase by a factor of ∼5 the number of such events within the Herschel-ATLAS data set. Although the methodology can be applied to address several selection problems, it has particular benefits in the case of the identification of strongly lensed galaxies: objectivity, minimal initial constrains in the main parameter space, and preservation of statistical properties. Methods. The proposed methodology is based on the Bhattacharyya distance as a measure of the similarity between probability distributions of properties of two different cross-matched galaxies. The particular implementation for the aim of this work is called SHALOS and it combines the information of four different properties of the pair of galaxies: angular separation, luminosity percentile, redshift, and the ratio of the optical to the submillimetre flux densities. Results. The SHALOS method provides a ranked list of strongly lensed galaxies. The number of candidates within ∼340 deg2 of the Herschel-ATLAS surveyed area for the final associated probability, Ptot > 0.7, is 447 and they have an estimated mean amplification factor of 3.12 for a halo with a typical cluster mass. Additional statistical properties of the SHALOS candidates, as the correlation function or the source number counts, are in agreement with previous results indicating the statistical lensing nature of the selected sampleJGN acknowledges financial from the Spanish MINECO for a “Ramon y Cajal” fellowship (RYC2013-13256). DH, FA, and LT acknowledge financial support from the I+D 2015 project AYA2015-64508-P (MINECO, FEDER)

On manifolds with nonhomogeneous factors

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces

A note on fake surfaces and universal covers

AbstractIn this paper, we consider compact fake surfaces X with the property that each component of the subgraph Γ⊂X of triple edges contains at most one point whose link in X is homeomorphic to the 1-skeleton of a tetrahedron (type III). Assuming the subgroups Λi⊆π1(X) generated by the loops in Γ at the points vi of type III are of a certain kind, an application of F.F. Lasheras [Proc. Amer. Math. Soc. 128 (2000) 893–902; J. Pure Appl. Algebra 151 (2) (2000) 163–172] leads us to finding a compact polyhedron K with π1(K)≅π1(X) and whose universal cover K has the proper homotopy type of a 3-manifold. This result extends the work in F.F. Lasheras [J. Pure Appl. Algebra 151 (2) (2000) 163–172] about a question on finitely presented groups