32,862 research outputs found
Moment-angle complexes, monomial ideals, and Massey products
Associated to every finite simplicial complex K there is a "moment-angle"
finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth,
compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study
the cohomology ring, the homotopy groups, and the triple Massey products of a
moment-angle complex, relating these topological invariants to the algebraic
combinatorics of the underlying simplicial complex. Applications to the study
of non-formal manifolds and subspace arrangements are given.Comment: 30 pages. Published versio
On the homotopy Lie algebra of an arrangement
Let A be a graded-commutative, connected k-algebra generated in degree 1. The
homotopy Lie algebra g_A is defined to be the Lie algebra of primitives of the
Yoneda algebra, Ext_A(k,k). Under certain homological assumptions on A and its
quadratic closure, we express g_A as a semi-direct product of the
well-understood holonomy Lie algebra h_A with a certain h_A-module. This allows
us to compute the homotopy Lie algebra associated to the cohomology ring of the
complement of a complex hyperplane arrangement, provided some combinatorial
assumptions are satisfied. As an application, we give examples of hyperplane
arrangements whose complements have the same Poincar\'e polynomial, the same
fundamental group, and the same holonomy Lie algebra, yet different homotopy
Lie algebras.Comment: 20 pages; accepted for publication by the Michigan Math. Journa
Fitness-based network growth with dynamic feedback
This article is a preprint of a paper that is currently under review with Physical Review E.We study a class of network growth models in which the choice of attachment by new nodes is governed by intrinsic attractiveness, or tness, of the existing nodes. The key feature of the models is a feedback mechanism whereby the distribution from which fitnesses of new nodes are drawn is dynamically updated to account for the evolving degree distribution. It is shown that in the case of linear mapping between fitnesses and degrees, the models lead to tunable stationary powerlaw degree distribution, while in the non-linear case the distributions converge to the stretched exponential form
Galaxy Light Concentration. I. Index stability and the connection with galaxy structure, dynamics, and supermassive black holes
We explore the stability of different galaxy light concentration indices as a
function of the outermost observed galaxy radius. With a series of analytical
light-profile models, we show mathematically how varying the radial extent to
which one measures a galaxy's light can strongly affect the derived galaxy
concentration. The "mean concentration index", often used for parameterizing
high-redshift galaxies, is shown to be horribly unstable, even when modeling
one-component systems such as elliptical, dwarf elliptical and pure exponential
disk galaxies. The C_31 concentration index performs considerably better but is
also heavily dependent on the radial extent, and hence exposure depth, of any
given galaxy. We show that the recently defined central concentration index is
remarkably stable against changes to the outer radius, providing a meaningful
and reliable estimate of galaxy concentration. The index n from the r^(1/n)
models is shown to be monotonically related with the central concentration of
light, giving the index n a second and perhaps more tangible meaning. With a
sample of elliptical and dwarf elliptical galaxies, we present correlations
between the central light concentration and the global parameters: luminosity
(Pearson's r = -0.82), effective radius (r = 0.67), central surface brightness
(r = -0.88), and velocity dispersion (r = 0.80). The more massive elliptical
galaxies are shown to be more centrally concentrated. We speculate that the
physical mechanism behind the recently observed correlation between the central
velocity dispersion (mass) of a galaxy and the mass of its central supermassive
black hole may be connected with the central galaxy concentration. That is, we
hypothesize that it may not simply be the amount of mass in a galaxy but rather
how that mass is distributed that controls the mass of the central black hole.Comment: (aastex, 18 pages including 13 figures
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