Cohomological finiteness conditions for a class of metabelian groups

We consider a class of metabelian groups first studied by Baumslag and Stammbach and we show that these groups are consistent with the Bieri-Groves conjecture which relates cohomological finiteness conditions to the Bieri-Neumann-Strebel sigma invariant.Comment: 10 pages Accepted for publication in the Bulletin of the London Mathematical Societ

Picking a Winner? Evidence from the Non-Manufacturing High-Tech Industry in the Blacksburg MSA

Regional scientists have developed numerous concepts and measures of economic diversity and diversification, primarily motivated by the desire to establish a relationship between diversity and economic performance. Rather than striving for a unified theory with a singular measure, this paper argues that economic developers should employ a multi-dimensional framework that combines the comparative advantages of a range of theoretical approaches. The application of locational, agglomerational and risk-reward measures to the non-manufacturing high-tech industry for the Blacksburg MSA in southwestern Virginia reveals specific policy implications and offers lessons for economic policy design.Economic Development; Industry Concentration; Dispersion; Quantitative Measures

The Transformation Problem: A Tale of Two Interpretations

Over 100 years since Marx's value theory of labour was first published, the so-called ``transformation problem'' -- deriving prices from values and providing a theory of profits as arising from surplus value -- has inspired the imagination of economists of all shades of intellectual suasion. However, while mainstream economists have by and large come to dismiss the transformation problem as a trivial technical exercise, the issue has recently received renewed attention in Marxian economic theory. This paper provides a broad historical overview of the transformation problem and specifically focuses on similarities and differences of how the transformation problem has been interpreted, why it was put to rest in mainstream economics and how it has regained prominence in Marxian economics.History of Economic Thought; Marxian Economics; Value Theory of Labour

Limit sets for modules over groups on CAT(0) spaces -- from the Euclidean to the hyperbolic

The observation that the 0-dimensional Geometric Invariant $\Sigma ^{0}(G;A)$ of Bieri-Neumann-Strebel-Renz can be interpreted as a horospherical limit set opens a direct trail from Poincar\'e's limit set $\Lambda (\Gamma)$ of a discrete group $\Gamma$ of M\"obius transformations (which contains the horospherical limit set of $\Gamma$) to the roots of tropical geometry (closely related to $\Sigma ^{0}(G;A)$ when G is abelian). We explore this trail by introducing the horospherical limit set, $\Sigma (M;A)$, of a G-module A when G acts by isometries on a proper CAT(0) metric space M. This is a subset of the boundary at infinity of M. On the way we meet instances where $\Sigma (M;A)$ is the set of all conical limit points, the complement of a spherical building, the complement of the radial projection of a tropical variety, or (via the Bieri-Neumann-Strebel invariant) where it is closely related to the Thurston norm.Comment: This is the final published versio