Quasi-isometrically embedded subgroups of Thompson's group F

The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson's group $F$ which are isomorphic to \fz^n for all $n$. A result estimating the norm of an element of Thompson's group is found. As a corollary, Thompson's group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone.Comment: AMS-Tex file, 8 page

Molecular line probes of activity in galaxies

The use of specific tracers of the dense molecular gas phase can help to explore the feedback of activity on the interstellar medium (ISM) in galaxies. This information is a key to any quantitative assessment of the efficiency of the star formation process in galaxies. We present the results of a survey devoted to probe the feedback of activity through the study of the excitation and chemistry of the dense molecular gas in a sample of local universe starbursts and active galactic nuclei (AGNs). Our sample includes also 17 luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs). From the analysis of the LIRGs/ULIRGs subsample, published in Gracia-Carpio et al.(2007) we find the first clear observational evidence that the star formation efficiency of the dense gas, measured by the L_FIR/L_HCN ratio, is significantly higher in LIRGs and ULIRGs than in normal galaxies. Mounting evidence of overabundant HCN in active environments would even reinforce the reported trend, pointing to a significant turn upward in the Kennicutt-Schmidt law around L_FIR=10^11 L_sun. This result has major implications for the use of HCN as a tracer of the dense gas in local and high-redshift luminous infrared galaxies.Comment: 4 pages, 2 figures, contributed paper to Far-Infrared Workshop 07 (FIR 2007

Computational explorations in Thompson's group F

We describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.Comment: 16 pages, 2 figures, 5 table