2,598 research outputs found
Nonabelian cohomology jump loci from an analytic viewpoint
For a topological space, we investigate its cohomology support loci, sitting
inside varieties of (nonabelian) representations of the fundamental group. To
do this, for a CDG (commutative differential graded) algebra, we define its
cohomology jump loci, sitting inside varieties of (algebraic) flat connections.
We prove that the analytic germs at the origin 1 of representation varieties
are determined by the Sullivan 1-minimal model of the space. Under mild
finiteness assumptions, we show that, up to a degree , the two types of jump
loci have the same analytic germs at the origins, when the space and the
algebra have the same -minimal model. We apply this general approach to
formal spaces (for which we establish the degeneration of the Farber-Novikov
spectral sequence), quasi-projective manifolds, and finitely generated
nilpotent groups. When the CDG algebra has positive weights, we elucidate some
of the structure of (rank one complex) topological and algebraic jump loci: up
to degree , all their irreducible components passing through the origin are
connected affine subtori, respectively rational linear subspaces. Furthermore,
the global exponential map sends all algebraic cohomology jump loci, up to
degree , into their topological counterpart.Comment: New Corollary 1.7 added and Theorem D. strengthened. Final version,
to appear in Communications in Contemporary Mathematic
Arithmetic group symmetry and finiteness properties of Torelli groups
We examine groups whose resonance varieties, characteristic varieties and
Sigma-invariants have a natural arithmetic group symmetry, and we explore
implications on various finiteness properties of subgroups. We compute
resonance varieties, characteristic varieties and Alexander polynomials of
Torelli groups, and we show that all subgroups containing the Johnson kernel
have finite first Betti number, when the genus is at least four. We also prove
that, in this range, the -adic completion of the Alexander invariant is
finite-dimensional, and the Kahler property for the Torelli group implies the
finite generation of the Johnson kernel.Comment: Updated references, to appear in Ann. of Mat
Heuristic algorithms for the Longest Filled Common Subsequence Problem
At CPM 2017, Castelli et al. define and study a new variant of the Longest
Common Subsequence Problem, termed the Longest Filled Common Subsequence
Problem (LFCS). For the LFCS problem, the input consists of two strings and
and a multiset of characters . The goal is to insert the
characters from into the string , thus obtaining a new string
, such that the Longest Common Subsequence (LCS) between and is
maximized. Casteli et al. show that the problem is NP-hard and provide a
3/5-approximation algorithm for the problem.
In this paper we study the problem from the experimental point of view. We
introduce, implement and test new heuristic algorithms and compare them with
the approximation algorithm of Casteli et al. Moreover, we introduce an Integer
Linear Program (ILP) model for the problem and we use the state of the art ILP
solver, Gurobi, to obtain exact solution for moderate sized instances.Comment: Accepted and presented as a proceedings paper at SYNASC 201
Numerical Methods for Obtaining Multimedia Graphical Effects
This paper is an explanatory document about how several animations effects can be obtained using different numerical methods, as well as investigating the possibility of implementing them on very simple yet powerful massive parallel machines. The methods are clearly described, containing graphical examples of the effects, as well as workflow for the algorithms. All of the methods presented in this paper use only numerical matrix manipulations, which usually are fast, and do not require the use of any other graphical software application.raster graphics, numerical matrix manipulation, animation effects
Quasi-K\"ahler Bestvina-Brady groups
A finite simple graph \G determines a right-angled Artin group G_\G, with one
generator for each vertex v, and with one commutator relation vw=wv for each
pair of vertices joined by an edge. The Bestvina-Brady group N_\G is the kernel
of the projection G_\G \to \Z, which sends each generator v to 1. We establish
precisely which graphs \G give rise to quasi-K\"ahler (respectively, K\"ahler)
groups N_\G. This yields examples of quasi-projective groups which are not
commensurable (up to finite kernels) to the fundamental group of any
aspherical, quasi-projective variety.Comment: 11 pages, accepted for publication by the Journal of Algebraic
Geometr
Non-finiteness properties of fundamental groups of smooth projective varieties
For each integer n\ge 2, we construct an irreducible, smooth, complex
projective variety M of dimension n, whose fundamental group has infinitely
generated homology in degree n+1 and whose universal cover is a Stein manifold,
homotopy equivalent to an infinite bouquet of n-dimensional spheres. This
non-finiteness phenomenon is also reflected in the fact that the homotopy group
\pi_n(M), viewed as a module over Z\pi_1(M), is free of infinite rank. As a
result, we give a negative answer to a question of Koll'ar on the existence of
quasi-projective classifying spaces (up to commensurability) for the
fundamental groups of smooth projective varieties. To obtain our examples, we
develop a complex analog of a method in geometric group theory due to Bestvina
and Brady.Comment: 16 page
Alexander polynomials: Essential variables and multiplicities
We explore the codimension one strata in the degree-one cohomology jumping
loci of a finitely generated group, through the prism of the multivariable
Alexander polynomial. As an application, we give new criteria that must be
satisfied by fundamental groups of smooth, quasi-projective complex varieties.
These criteria establish precisely which fundamental groups of boundary
manifolds of complex line arrangements are quasi-projective. We also give sharp
upper bounds for the twisted Betti ranks of a group, in terms of multiplicities
constructed from the Alexander polynomial. For Seifert links in homology
3-spheres, these bounds become equalities, and our formula shows explicitly how
the Alexander polynomial determines all the characteristic varieties.Comment: 27 page
OPEN EDUCATIONAL RESOURCES MANAGEMENT (OERM)
Network communication and Internet have expanded the way in which education can be delivered to the learners of today. Today's networking technologies provide a valuable opportunity to the practice of learning techniques. Educators are discovering that computer networks and multibased educational tools are facilitating learning and enhancing social interaction. Network based telecommunications can offer enormous instructional opportunities, and the educators will need to adapt current lesson plan to incorporate this new medium into all their classes.management, educational resources
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