Characteristic varieties and Betti numbers of free abelian covers

The regular \Z^r-covers of a finite cell complex X are parameterized by the Grassmannian of r-planes in H^1(X,\Q). Moving about this variety, and recording when the Betti numbers b_1,..., b_i of the corresponding covers are finite carves out certain subsets \Omega^i_r(X) of the Grassmannian. We present here a method, essentially going back to Dwyer and Fried, for computing these sets in terms of the jump loci for homology with coefficients in rank 1 local systems on X. Using the exponential tangent cones to these jump loci, we show that each \Omega-invariant is contained in the complement of a union of Schubert varieties associated to an arrangement of linear subspaces in H^1(X,\Q). The theory can be made very explicit in the case when the characteristic varieties of X are unions of translated tori. But even in this setting, the \Omega-invariants are not necessarily open, not even when X is a smooth complex projective variety. As an application, we discuss the geometric finiteness properties of some classes of groups.Comment: 40 pages, 2 figures; accepted for publication in International Mathematics Research Notice

Resonance varieties and Dwyer-Fried invariants

The Dwyer-Fried invariants of a finite cell complex X are the subsets \Omega^i_r(X) of the Grassmannian of r-planes in H^1(X,\Q) which parametrize the regular \Z^r-covers of X having finite Betti numbers up to degree i. In previous work, we showed that each \Omega-invariant is contained in the complement of a union of Schubert varieties associated to a certain subspace arrangement in H^1(X,\Q). Here, we identify a class of spaces for which this inclusion holds as equality. For such "straight" spaces X, all the data required to compute the \Omega-invariants can be extracted from the resonance varieties associated to the cohomology ring H^*(X,\Q). In general, though, translated components in the characteristic varieties affect the answer.Comment: 39 pages; to appear in "Arrangements of Hyperplanes - Sapporo 2009," Advanced Studies in Pure Mathematic

Fundamental groups, Alexander invariants, and cohomology jumping loci

We survey the cohomology jumping loci and the Alexander-type invariants associated to a space, or to its fundamental group. Though most of the material is expository, we provide new examples and applications, which in turn raise several questions and conjectures. The jump loci of a space X come in two basic flavors: the characteristic varieties, or, the support loci for homology with coefficients in rank 1 local systems, and the resonance varieties, or, the support loci for the homology of the cochain complexes arising from multiplication by degree 1 classes in the cohomology ring of X. The geometry of these varieties is intimately related to the formality, (quasi-) projectivity, and homological finiteness properties of \pi_1(X). We illustrate this approach with various applications to the study of hyperplane arrangements, Milnor fibrations, 3-manifolds, and right-angled Artin groups.Comment: 45 pages; accepted for publication in Contemporary Mathematic

Similarities and Differences Between Internal Auditing, Internal Public Auditing and Other Services

The internal auditing is an independent, objective assurance and consulting activity designed to add value and improve an organization's operations. It helps an organization accomplish its objectives by bringing a systematic, disciplined approach to evaluate and improve the effectiveness of risk management, control, and governance processes, making propositions in order to consolidate the efficiency. The financial auditing represents the activity of professional examination of the information in the purpose of expressing a responsible and independent opinion, in relation to a standard, quality criteria aiming at improving the use of information. The Internal public auditing helps the public entity to fulfill its goals through a systematic and methodic approach, evaluating and improving the efficiency of the management system based on risk, control and administration processes management. The control represents a permanent or periodical analysis of the activity, of the situation in order to follow its development and in order to take improvement measures.internal auditing, internal public auditing, external audit, internal control.

Intellectual capital as a source of the competitive advantage

The main aim of the paper is to provide a synthesis of the new international framework of debate dedicated to intellectual capital. New economics and knowledge-based society focus on a portfolio of intangible assets to be managed. Intellectual capital is the essential root system of competitiveness, but is often invisible in the traditional accounting systems. The paper presents some examples of how to measure, report and monitor intellectual capital.intellectual capital; management of intellectual capital; new economics