2,131 research outputs found
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 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 -manifold admitting a simple crystallization
admits a special handlebody decomposition, too; equivalently, may be
represented by a framed link yielding , with exactly
components ( being the second Betti number of ). As a
consequence, the regular genus of is proved to be the double of
. Moreover, the characterization of any such PL -manifold by
, where is the gem-complexity of (i.e. the
non-negative number , being the minimum order of a crystallization of
) implies that both PL invariants gem-complexity and regular genus turn out
to be additive within the class of all PL -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
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
Combinatorial properties of the G-degree
A strong interaction is known to exist between edge-colored graphs (which encode PL pseudo-manifolds of arbitrary dimension) and random tensor models (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 tensor models context. In the present paper - by making use of combinatorial properties concerning Hamiltonian decompositions of the complete graph - we prove that, in any even dimension d greater or equal to 4, the G-degree of all bipartite graphs, as well as of all (bipartite or non-bipartite) graphs representing singular manifolds, is an integer multiple of (d-1)!. As a consequence, in even dimension, the terms of the 1/N expansion corresponding to odd powers of 1/N are null in the complex context, and do not involve colored graphs representing singular manifolds in the real context. In particular, in the 4-dimensional case, where the G-degree is shown to depend only on the regular genera with respect to an arbitrary pair of "associated" cyclic permutations, several results are obtained, relating the G-degree or the regular genus of 5-colored graphs and the Euler characteristic of the associated PL 4-manifolds
Uniform random colored complexes
We present here random distributions on -edge-colored, bipartite
graphs with a fixed number of vertices . These graphs are dual to
-dimensional orientable colored complexes. We investigate the behavior of
quantities related to those random graphs, such as their number of connected
components or the number of vertices of their dual complexes, as . The techniques involved in the study of these quantities also yield a
Central Limit Theorem for the genus of a uniform map of order , as .Comment: 36 pages, 9 figures, minor additions and correction
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
A Tolman Surface Brightness Test for Universal Expansion, and the Evolution of Elliptical Galaxies in Distant Clusters
We use the intercept of the elliptical galaxy radius--surface brightness (SB)
relation at a fixed metric radius as the standard condition for the Tolman SB
test of the universal expansion. We use surface photometry in the optical and
near-IR of elliptical galaxies in Abell~2390 () and Abell~851
(), and compare them to the Coma cluster at . The
photometric data for each cluster are well-described by the Kormendy relation
, where in the optical and in the
near-IR. The scatter about this near-IR relation is only in
at the highest redshift, which is much smaller than at low redshifts,
suggesting a remarkable homogeneity of the cluster elliptical population at
. We use the intercept of these fixed-slope correlations at ~kpc (assuming ~km~s~Mpc, , and
, where the results are only weakly dependent on the cosmology) to
construct the Tolman SB test for these three clusters. The data are fully
consistent with universal expansion if we assume simple models of passive
evolution for elliptical galaxies, but are inconsistent with a non-expanding
geometry (the tired light cosmology) at the confidence level at
. These results suggest luminosity evolution in the restframe -band
of ~mag from to the present, and are consistent with
the ellipticals having formed at high redshift. The SB intercept in elliptical
galaxy correlations is thus a powerful tool for investigating models of their
evolution for significant lookback times.Comment: to appear in The Astrophysical Journal (Letters); 13 pages, including
3 Postscript figures and 1 table; uuencoded, compressed format; the paper is
also available in various formats from
http://astro.caltech.edu/~map/map.bibliography.refereed.htm
The Infrared Surface Brightness Fluctuation Distances to the Hydra and Coma Clusters
We present IR surface brightness fluctuation (SBF) distance measurements to
NGC 4889 in the Coma cluster and to NGC 3309 and NGC 3311 in the Hydra cluster.
We explicitly corrected for the contributions to the fluctuations from globular
clusters, background galaxies, and residual background variance. We measured a
distance of 85 +/- 10 Mpc to NGC 4889 and a distance of 46 +/- 5 Mpc to the
Hydra cluster. Adopting recession velocities of 7186 +/- 428 km/s for Coma and
4054 +/- 296 km/s for Hydra gives a mean Hubble constant of H_0 = 87 +/- 11
km/s/Mpc. Corrections for residual variances were a significant fraction of the
SBF signal measured, and, if underestimated, would bias our measurement towards
smaller distances and larger values of H_0. Both NICMOS on the Hubble Space
Telescope and large-aperture ground-based telescopes with new IR detectors will
make accurate SBF distance measurements possible to 100 Mpc and beyond.Comment: 24 pages, 4 PostScript figures, 2 JPEG images; accepted for
publication in Ap
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