Euler Obstruction and Defects of Functions on Singular Varieties

Several authors have proved Lefschetz type formulae for the local Euler obstruction. In particular, a result of this type is proved in [BLS].The formula proved in that paper turns out to be equivalent to saying that the local Euler obstruction, as a constructible function, satisfies the local Euler condition (in bivariant theory) with respect to general linear forms. The purpose of this work is to understand what prevents the local Euler obstruction of satisfying the local Euler condition with respect to functions which are singular at the considered point. This is measured by an invariant (or ``defect'') of such functions that we define below. We give an interpretation of this defect in terms of vanishing cycles, which allows us to calculate it algebraically. When the function has an isolated singularity, our invariant can be defined geometrically, via obstruction theory. We notice that this invariant unifies the usual concepts of {\it the Milnor number} of a function and of the {\it local Euler obstruction} of an analytic set.Comment: 18 page

An overview on complex Kleinian groups

Classical Kleinian groups are discrete subgroups of PSL(2,\C) acting on the complex projective line $\P^1$, which actually coincides with the Riemann sphere, with non-empty region of discontinuity. These can also be regarded as the monodromy groups of certain differential equations. These groups have played a major role in many aspects of mathematics for decades, and also in physics. It is thus natural to study discrete subgroups of the projective group PSL(n,\C), $n > 2$. Surprisingly, this is a branch of mathematics which is in its childhood, and in this article we give an overview of it

Real map germs and higher open books

We present a general criterion for the existence of open book structures defined by real map germs (\bR^m, 0) \to (\bR^p, 0), where $m> p \ge 2$, with isolated critical point. We show that this is satisfied by weighted-homogeneous maps. We also derive sufficient conditions in case of map germs with isolated critical value.Comment: 12 page

Spherical Universe topology and the Casimir effect

The mode problem on the factored 3--sphere is applied to field theory calculations for massless fields of spin 0, 1/2 and 1. The degeneracies on the factors, including lens spaces, are neatly derived in a geometric fashion. Vacuum energies are expressed in terms of the polyhedral degrees and equivalent expressions given using the cyclic decomposition of the covering group. Scalar functional determinants are calculated and the spectral asymmetry function treated by the same approach with explicit forms on one-sided lens spaces.Comment: 33 pages, 1 figure. Typos corrected and one reference adde

Optimal redistributive tax and education policies in general equilibrium

This paper studies optimal linear and non-linear income taxes and education subsidies in two-type models with endogenous human capital formation, endogenous labor supply, and endogenous wage rates. Assuming constant human capital elasticities, human capital investment should be efficient under optimal linear policies, whether general equilibrium effects are present or not. Hence, education subsidies should not be used for distributional reasons. Due to general equilibrium effects, optimal linear income taxes may even become negative. Optimal non-linear policies exploit general equilibrium effects for redistribution. The high-skilled type optimally has a negative marginal income tax rate and a positive marginal education subsidy. The low-skilled type optimally faces a positive marginal income tax rate and a marginal tax on education. Simulations demonstrate that general equilibrium effects have only a modest effect on optimal non-linear policies

Anosov representations: Domains of discontinuity and applications

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation of $\Gamma$ into G we explicitly construct open subsets of compact G-spaces, on which $\Gamma$ acts properly discontinuously and with compact quotient. As a consequence we show that higher Teichmueller spaces parametrize locally homogeneous geometric structures on compact manifolds. We also obtain applications regarding (non-standard) compact Clifford-Klein forms and compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica

Taxation and market power

"We analyze the incidence and welfare effects of unit sales taxes in experimental monopoly and Bertrand markets. We find, in line with economic theory, that firms with no market power are able to shift a high share of a tax burden on to consumers, independent of whether buyers are automated or human players. In monopoly markets, a monopolist bears a large share of the burden of a tax increase. With human buyers, however, this share is smaller than with automated buyers as the presence of human buyers constrains the pricing behavior of a monopolist." (author's abstract)"Dieser Artikel untersucht Inzidenz- und Wohlfahrtseffekte einer Mengensteuer in experimentellen Monopol- und Bertrand-Märkten. Im Einklang mit der ökonomischen Theorie sind Firmen ohne Marktmacht in der Lage, einen großen Anteil der Last einer Steuererhöhung an die Konsumenten weiterzugeben. Dies gilt unabhängig davon, ob die Käufer simuliert sind oder die Kaufentscheidungen durch reale Käufer getroffen werden. In Monopolmärkten trägt der Monopolist einen großen Anteil der Last einer Steuererhöhung. Werden die Kaufentscheidungen durch reale Käufer getroffen, ist dieser Anteil jedoch kleiner als mit simulierten Käufern, da reale Käufer im Experiment das Preissetzungsverhalten des Monopolisten einschränken." (Autorenreferat