Cataloguing PL 4-manifolds by gem-complexity

We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogue of all closed connected PL 4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation with at most 18 4-simplices). Possible interactions with the (not completely known) relationship among different classification in TOP and DIFF=PL categories are also investigated. As a first consequence of the above PL classification, the non-existence of exotic PL 4-manifolds up to gem-complexity 8 is proved. Further applications of the tool are described, related to possible PL-recognition of different triangulations of the K3-surface.Comment: 25 pages, 5 figures. Improvements suggested by the refere

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

High Resolution Near-Infrared Spectra of Protostars

We present new high resolution (R = 21,000) near-infrared (2 microns) spectroscopic observations of a sample of Class I and flat-spectrum protostellar objects in the rho Ophiuchi dark cloud. None of the five Class I spectra show CO v = 0 -- 2 absorption features, consistent with high K-band continuum veilings, 4 <= r_k <= 20 and fast stellar rotation, assuming that the underlying protostellar photospheres are of late spectral type, as is suggested by the low luminosities of most of these objects. Two of the flat-spectrum protostellar objects also show no absorption features and are likely to be highly veiled. The remaining two flat-spectrum sources show weak, broad absorptions which are consistent with an origin in quickly rotating (v sin i ~ 50 km / s) late-type stellar photospheres which are also strongly veiled, r_k = 3 - 4. These observations provide further evidence that: 1)-Class I sources are highly veiled at near-infrared wavelengths, confirming previous findings of lower resolution spectroscopic studies; and 2)- flat-spectrum protostars rotate more rapidly than classical T Tauri stars (Class II sources), supporting findings from a recent high resolution spectroscopic study of other flat-spectrum sources in this cloud. In addition our observations are consistent with the high rotation rates derived for two of the Class I protostellar objects in our sample from observations of variable hard X-ray emission obtained with the ASCA satellite. These observations suggest that certain Class I sources can rotate even more rapidly than flat-spectrum protostars, near breakup velocity.Comment: 16 pages including 2 tables and 2 figures (AASTeX 5.x) to be published in The Astronomical Journal July 200

VIRIS: A Visual-Infrared Imaging System for the Lick Observatory 1-M Telescope

We describe a system in use at the Lick Observatory 1-m Nickel telescope for near-simultaneous imaging at optical and near-infrared wavelengths. The combined availability of a CCD and a NICMOS-3 camera makes the system well-suited for photometric monitoring from 0.5-2.2 microns of a variety of astrophysical objects. Our science program thus far has concentrated on studying variability trends in young stellar objects.Comment: 11 pages LaTex, 3 Postscript figure, Pub. Astr. Soc. Pac. 1998, in pres

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

A Companion Galaxy to the Post-Starburst Quasar UN J1025-0040

UN J1025-0040 is a quasar at z = 0.6344 that shows an extremely bright post starburst population of age ~ 400 Myr (Brotherton et al. 1999). Images of UN J1025-0040 show a nearly stellar object 4.2 arcseconds SSW of the quasar. We present imaging and spectroscopy that confirm that this object is a companion galaxy at redshift z = 0.6341. We estimate an age of ~ 800 Myr for the dominant stellar population in the companion. The companion appears to be interacting with the quasar host galaxy, and this interaction may have triggered both the starburst and the quasar activity in UN J1025-0040.Comment: 8 pages plus 4 figures (2 postscript, 2 jpg). Postscript version available at http://www.ifa.hawaii.edu/~canaguby/preprints.html To appear in the January 2000 issue of A

PG 1700+518 Revisited: Adaptive Optics Imaging and a Revised Starburst Age for the Companion

We present the results of adaptive-optics imaging of the z=0.2923 QSO PG 1700+518 in the J and H bands. The extension to the north of the QSO is clearly seen to be a discrete companion with a well-defined tidal tail, rather than a feature associated with the host galaxy of PG 1700+518 itself. On the other hand, an extension to the southwest of the QSO (seen best in deeper, but lower-resolution, optical images) does likely comprise tidal material from the host galaxy. The SED derived from images in J, H, and two non-standard optical bands indicates the presence of dust intermixed with the stellar component. We use our previously reported Keck spectrum of the companion, the SED found from the imaging data, and updated spectral-synthesis models to constrain the stellar populations in the companion and to redetermine the age of the starburst. While our best-fit age of 0.085 Gyr is nearly the same as our earlier determination, the fit of the new models is considerably better. This age is found to be remarkably robust with respect to different assumptions about the nature of the older stellar component and the effects of dust.Comment: 11 pages; includes two eps figures. Latex (AASTEX). Two additional figures in gif format. Postscript version including all figs. (424 kb) can be obtained from http://www.ifa.hawaii.edu/~canaguby/preprints.html To appear in ApJ. Letter