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

PL 4-manifolds admitting simple crystallizations: framed links and regular genus

Simple crystallizations are edge-coloured graphs representing PL 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simplex. In the present paper, we prove that any (simply-connected) PL $4$-manifold $M$ admitting a simple crystallization admits a special handlebody decomposition, too; equivalently, $M$ may be represented by a framed link yielding $\mathbb S^3$, with exactly $\beta_2(M)$ components ($\beta_2(M)$ being the second Betti number of $M$). As a consequence, the regular genus of $M$ is proved to be the double of $\beta_2(M)$. Moreover, the characterization of any such PL $4$-manifold by $k(M)= 3 \beta_2(M)$, where $k(M)$ is the gem-complexity of $M$ (i.e. the non-negative number $p-1$, $2p$ being the minimum order of a crystallization of $M$) implies that both PL invariants gem-complexity and regular genus turn out to be additive within the class of all PL $4$-manifolds admitting simple crystallizations (in particular: within the class of all "standard" simply-connected PL 4-manifolds).Comment: 14 pages, no figures; this is a new version of the former paper "A characterization of PL 4-manifolds admitting simple crystallizations

A Contracting, Turbulent, Starless Core in the Serpens Cluster

We present combined single-dish and interferometric CS(2--1) and N2H+(1--0) observations of a compact core in the NW region of the Serpens molecular cloud. The core is starless according to observations from optical to millimeter wavelengths and its lines have turbulent widths and ``infall asymmetry''. Line profile modeling indicates supersonic inward motions v_in>0.34 km/s over an extended region L>12000AU. The high infall speed and large extent exceeds the predictions of most thermal ambipolar diffusion models and points to a more dynamical process for core formation. A short (dynamic) timescale, ~1e5 yr=L/v_in, is also suggested by the low N2H+ abundance ~1e-10.Comment: 11 pages including 2 figures. Accepted for publication in the Astrophysical Journal Letter

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

By means of a slight modification of the notion of GM-complexity introduced in [Casali, M.R., Topol. Its Appl., 144: 201-209, 2004], the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C-28 available in [Lins, S., Knots and Everything 5, World Scientific, Singapore, 1995] is used to obtain upper bounds for the complexity of closed orientable 3-manifolds triangulated by at most 28 tetrahedra. The experimental results actually coincide with the exact values of complexity, for all but three elements. Moreover, in the case of at most 26 tetrahedra, the exact value of the complexity is shown to be always directly computable via crystallization theory

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

VLA 3.5 cm continuum sources in the Serpens cloud core

We present VLA 3.5 cm continuum observations of the Serpens cloud core. 22 radio continuum sources are detected. 16 out of the 22 cm sources are suggested to be associated with young stellar objects (Class 0, Class I, flat-spectrum, and Class II) of the young Serpens cluster. The rest of the VLA sources plausibly are background objects. Most of the Serpens cm sources likely represent thermal radio jets; on the other hand, the radio continuum emission of some sources could be due to a gyrosynchroton mechanism arising from coronally active young stars. The Serpens VLA sources are spatially distributed into two groups; one of them located towards the NW clump of the Serpens core, where only Class 0 and Class I protostars are found to present cm emission, and a second group located towards the SE clump, where radio continuum sources are associated with objects in evolutionary classes from Class 0 to Class II. This subgrouping is similar to that found in the near IR, mid-IR and mm wavelength regimes.Comment: 2 figures, accepted by Astronomical journa

Measurements of the Cerenkov light emitted by a TeO2 crystal

Bolometers have proven to be good instruments to search for rare processes because of their excellent energy resolution and their extremely low intrinsic background. In this kind of detectors, the capability of discriminating alpha particles from electrons represents an important aspect for the background reduction. One possibility for obtaining such a discrimination is provided by the detection of the Cerenkov light which, at the low energies of the natural radioactivity, is only emitted by electrons. In this paper, the results of the analysis of the light emitted by a TeO2 crystal at room temperature when transversed by a cosmic ray are reported. Light is promptly emitted after the particle crossing and a clear evidence of its directionality is also found. These results represent a strong indication that Cerenkov light is the main, if not even the only, component of the light signal in a TeO2 crystal. They open the possibility to make large improvements in the performance of experiments based on this kind of material

Infrared Surface Brightness Fluctuations of the Coma Elliptical NGC 4874 and the Value of the Hubble Constant

We have used the Keck I Telescope to measure K-band surface brightness fluctuations (SBFs) of NGC 4874, the dominant elliptical galaxy in the Coma cluster. We use deep HST WFPC2 optical imaging to account for the contamination due to faint globular clusters and improved analysis techniques to derive measurements of the SBF apparent magnitude. Using a new SBF calibration which accounts for the dependence of K-band SBFs on the integrated color of the stellar population, we measure a distance modulus of 34.99+/-0.21 mag (100+/-10 Mpc) for the Coma cluster. The resulting value of the Hubble constant is 71+/-8 km/s/Mpc, not including any systematic error in the HST Cepheid distance scale.Comment: ApJ Letters, in press. Uses emulateapj5.st