On the Tits alternative for PD(3)PD(3) groups

We prove the Tits alternative for an almost coherent $PD(3)$ group which is not virtually properly locally cyclic. In particular, we show that an almost coherent $PD(3)$ group which cannot be generated by fewer than four elements always contains a rank 2 free group.Comment: 16 pages, minor corrections, to appear in Ann. Fac. Sci. Toulouse Mat

On invertible generating pairs of fundamental groups of graph manifolds

We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g,h) for which the map g --> g^{-1}, h --> h^{-1} extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pair.Comment: This is the version published by Geometry & Topology Monographs on 29 April 200

The profinite completion of 33-manifold groups, fiberedness and the Thurston norm

We show that a regular isomorphism of profinite completion of the fundamental groups of two 3-manifolds $N_1$ and $N_2$ induces an isometry of the Thurston norms and a bijection between the fibered classes. We study to what extent does the profinite completion of knot groups distinguish knots and show that it distinguishes each torus knot and the figure eight knot among all knots. We show also that it distinguishes between hyperbolic knots with cyclically commensurable complements under the assumption that their Alexander polynomials have at least one zero which is not a root of unity.Comment: 22 page

The Current Account and the Interest Differential In Canada

For post-1975 Canadian data, we document the joint behavior of output, the current account, and the interest differential at the business cycle frequency. We also interpret the joint behavior using a simple small open economy model. Our simple model assumes that agents have access to world international financial markets, but face country-specific interest rate on their holdings of world assets. The interest differential depends negatively on the country’s net foreign asset position. We find that our simple model matches the Canadian data remarkably well.International Real Business Cycle, Small Open Economy, Habit Formation.

Closing International Real Business Cycle Models with Restricted Financial Markets

Several authors argue that international real business cycle (IRBC) models with incomplete financial markets offer a good explanation of the ranking of cross-country correlations. Unfortunately, this conclusion is suspect, because it is commonly based on an analysis of the near steady state dynamics using a linearized system of equations. The baseline IRBC model with incomplete financial markets does not possess a unique deterministic steady state and, as a result, its linear system of difference equations is not stationary. We show that the explanation of the ranking of cross-country correlations is robust to modifications that ensure a unique steady state and a stationary system of linear difference equations. We find, however, that the modifications affect the quantitative predictions regarding key macroeconomic variables.Incomplete markets, stationarity, cross-country correlations, wealth effects.

Closing International Real Business Cycle Models with Restricted Financial Markets

Several authors argue that international real business cycle (IRBC) models with incomplete financial markets offer a good explanation of the ranking of cross-country correlations. Unfortunately, this conclusion is suspect, because it is commonly based on an analysis of the near steady state dynamics using a linearized system of equations. The baseline IRBC model with incomplete financial markets does not possess a unique deterministic steady state and, as a result, its linear system of difference equations is not stationary. We show that the explanation of the ranking of cross-country correlations is robust to modifications that ensure a unique steady state and a stationary system of linear difference equations. We find, however, that the modifications affect the quantitative predictions regarding key macroeconomic variables.Incomplete markets, stationarity, cross-country correlations, wealth effects

Dynamics of the Current Account and Interest Differentials

In contrast to earlier work, we study the relation between the current account and interest rate differentials. To do so, we document the relation for international data. We then interpret this relation from a two-country, dynamic, general equilibrium environment. We finally confront the relation predicted by the environment to the relation observed in the data. We find that the environmental correctly predicts that the current account is countercyclical; that the interest differentials is procyclical; and that the current account is negatively correlated with current and future interest differentials, but positively correlated with past interest differentials.International real business cycle

Degree one maps between small 3-manifolds and Heegaard genus

We prove a rigidity theorem for degree one maps between small 3-manifolds using Heegaard genus, and provide some applications and connections to Heegaard genus and Dehn surgery problems.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-56.abs.htm