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

The role of social capital in fishing community sustainability: case of Shelter Cove, CA

Community development scholars have consistently highlighted the importance of social capital – the glue that keeps a community together – for the development and long-term sustainability of rural communities. There has been less discussion about the role of social capital in fishing communities. This thesis explores the historical trajectory of social capital in Shelter Cove, CA, a small, remote fishing community with an attempt to understand how the type and level of social capital have and may continue to affect the progress and sustainability of the community. Data for this thesis were collected as part of a strategic planning effort in the Shelter Cove fishing community that documented community members’ perceptions of the current state of this fishing community and recommendations of how things could be improved. Interview data from the Shelter Cove Fishing Community Sustainability Plan (FCSP) were analyzed to provide the 2017 to 2018 context of participants’ perceptions of the fishing community. Research methods included semi-structured interviews with 50 individuals, three public workshops, and document review and archival research. These data were paired with additional document review and historical analysis of the path that led the community to its current state of social capital. Both of these data streams were qualitatively coded to find emergent themes. Social capital emerged as an area for capital asset development that had been strong historically, but that has eroded over time as a result of a multitude of events that left the fishing community less resilient to unforeseen changes. This thesis provides general pathways and recommendations for rural fishing communities to invest further in their social capital assets through both bonding and bridging social networks to prepare them to be more sustainable fishing communities in the future

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

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 ($z=0.23$) and Abell~851 ($z=0.41$), and compare them to the Coma cluster at $z\approx 0$. The photometric data for each cluster are well-described by the Kormendy relation $r_e \propto \Sigma_e^{A}$, where $A=-0.9$ in the optical and $A=-1.0$ in the near-IR. The scatter about this near-IR relation is only $0.076$ in $\log r_e$ at the highest redshift, which is much smaller than at low redshifts, suggesting a remarkable homogeneity of the cluster elliptical population at $z=0.41$. We use the intercept of these fixed-slope correlations at $R_e = 1$~kpc (assuming $H_0=75$~km~s$^{-1}$~Mpc$^{-1}$, $\Omega_0=0.2$, and $\Lambda_0=0$, 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 $5 \, \sigma$ confidence level at $z=0.41$. These results suggest luminosity evolution in the restframe $K$-band of $0.36 \pm 0.14$~mag from $z = 0.41$ 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