We consider various problems regarding roots and coincidence points for maps into the Klein bottle K . The root problem where the target is K and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from K to K is established, and we also obtain the following 1-...

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Mar...

Suppose M is a compact connected odd-dimensional manifold with boundary, whose interior M comes with a complete hyperbolic metric of finite volume. We will show that the L2-topological torsion of M and the L2-analytic torsion of the Riemannian manifold M are equal. In particular, the L2-topological torsion of M is proportional to the hyperbolic volume of M , with a constant of proportionality w...

We define and count lattice points in the moduli spaceMg,n of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli spaceMg,n. The enumeration produces polynomials with top degree coefficients tautological intersection numbers onMg,n and constant term the orbifold Euler characteristic ofMg,n. We also prove a recursive formula...

In this paper we exploit the specific structure of the Euler equation and develop two alternative GMM estimators that deal explicitly with measurement error. The first estimator assumes that the measurement error is lognormally distributed. The second estimator drops the distributional assumption and solves out for the unknown, but constant, conditional mean. Our monte carlo results suggest tha...

There should be a Grothendieck topology for an arithmetic scheme X such that the Euler characteristic of the cohomology groups of the constant sheaf Z with compact support at infinity gives, up to sign, the leading term of the zeta-function of X at s D 0. We construct a topology (the Weil-étale topology) for the ring of integers in a number field whose cohomology groups H i .Z/ determine such a...