Computing Matveev's complexity via crystallization theory: the boundary case

The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In this paper we extend the definition to the case of non-empty boundary and prove that for each compact irreducible and boundary-irreducible 3-manifold it coincides with the modified Heegaard complexity introduced by Cattabriga, Mulazzani and Vesnin. Moreover, via Gem-Matveev complexity, we obtain an estimation of Matveev's complexity for all Seifert 3-manifolds with base $\mathbb D^2$ and two exceptional fibers and, therefore, for all torus knot complements.Comment: 27 pages, 14 figure

TOPOLOGY IN COLORED TENSOR MODELS

From a “geometric topology” point of view, the theory of manifold representation by means of edge-colored graphs has been deeply studied since 1975 and many results have been achieved: its great advantage is the possibility of encoding, in any dimension, every PL d-manifold by means of a totally combinatorial tool. Edge-colored graphs also play an important rôle within colored tensor models theory, considered as a possible approach to the study of Quantum Gravity: the key tool is the G-degree of the involved graphs, which drives the 1/N expansion in the higher dimensional tensor models context, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting. Therefore, topological and geometrical properties of the represented PL manifolds, with respect to the G-degree, have specific relevance in the tensor models framework, show- ing a direct fruitful interaction between tensor models and discrete geometry, via edge-colored graphs. In colored tensor models, manifolds and pseudomanifolds are (almost) on the same footing, since they constitute the class of polyhedra represented by edge-colored Feynman graphs arising in this context; thus, a promising research trend is to look for classification results concerning all pseudomanifolds - or, at least, singular d-manifolds, if d ≥ 4 - represented by graphs of a given G-degree. In dimension 4, the existence of colored graphs encoding different PL manifolds with the same underlying TOP manifold, suggests also to investigate the ability of ten- sor models to accurately reflect geometric degrees of freedom of Quantum Gravity

Compact 3-manifolds via 4-colored graphs

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the eighties by S. Lins for closed 3-manifolds, which is in turn dual to the earlier construction introduced by Pezzana's school in Modena. In this context we establish some results concerning fundamental groups, connected sums, moves between graphs representing the same manifold, Heegaard genus and complexity, as well as an enumeration and classification of compact 3-manifolds representable by graphs with few vertices ($\le 6$ in the non-orientable case and $\le 8$ in the orientable one).Comment: 25 pages, 11 figures; changes suggested by referee: references added, figure 2 modified, results about classification of the manifolds in Proposition 17 announced at the end of section 9. Accepted for publication in RACSAM. The final publication is available at Springer (see DOI

Environmentally Friendly Sunscreens: Mechanochemical Synthesis and Characterization of β-CD Inclusion Complexes of Avobenzone and Octinoxate with Improved Photostability

We report on the mechanochemical synthesis of inclusion complexes obtained by reacting β-cyclodextrin (β-CD) with two widely used sunscreens, namely, avobenzone (AVO) and octinoxate (OCT). Formation of crystalline inclusion complexes was confirmed via a combination of solid-state techniques, including X-ray diffraction (XRD), Raman, and ATR-FTIR spectroscopies. A new, metastable polymorph of avobenzone was also isolated and characterized. NMR spectroscopy and thermal analyses (TGA and DSC) allowed us to evaluate the host/guest ratio and the water content (ca. 8H2O) in crystalline (β-CD)2·AVO and (β-CD)3·OCT2. Photodegradation of the two sunscreens upon inclusion in the hydrophobic cavity of β-CD was evaluated in solution via mass spectrometry (ESI-MS) and UV-vis spectroscopy and found to be sharply reduced. All findings indicate that the inclusion of AVO and OCT in β-CD might represent a viable route for the preparation of environmentally friendly sunscreens with improved photostability to be used in formulations of sun creams

Near-Infrared Adaptive Optics Imaging of the Central Regions of Nearby Sc Galaxies: I. M33

Near-infrared images obtained with the Canada-France-Hawaii Telescope (CFHT) Adaptive Optics Bonnette (AOB) are used to investigate the stellar content within 18 arcsec of the center of the Local Group spiral galaxy M33. AGB stars with near-infrared spectral-energy distributions similar to those of giants in the solar neighborhood and Baade's Window are detected over most of the field. The bolometric luminosity function (LF) of these stars has a discontinuity near M_{bol} = -5.25, and comparisons with evolutionary tracks suggest that most of the AGB stars formed in a burst of star formation 1 - 3 Gyr in the past. The images are also used to investigate the integrated near-infrared photometric properties of the nucleus and the central light concentration. The nucleus is bluer than the central light concentration, in agreement with previous studies at visible wavelengths. The CO index of the central light concentration 0.5 arcsec from the galaxy center is 0.05, which corresponds to [Fe/H] = -1.2 for simple stellar systems. Hence, the central light concentration could not have formed from the chemically-enriched material that dominates the present-day inner disk of M33.Comment: 23 pages of text + 11 figures; to appear in A

Detecting high redshift evolved galaxies as the hosts of optically faint hard X-ray sources

We combine deep Subaru near-infrared images of the massive lensing clusters A2390 and A370 with Keck optical data to map the spectral energy distributions (SEDs) of Chandra X-ray sources lying behind the clusters. The three sources behind A2390 are found to have extremely red colors with SEDs consistent with evolved galaxies at redshifts z>1.4. One source has extremely anomalous colors, which we interpret as evidence for a type Sa SED at a redshift around 2.5. The photometric redshift of another source has been confirmed at z=1.467 from near-infrared spectroscopy using the CISCO spectrograph on Subaru. Mapping of optically faint hard X-ray sources may prove to be an extremely efficient way to locate luminous evolved galaxies at high redshifts.Comment: 5 pages, ApJ Letters, in pres