For a bounded domain Ω ⊂ Rm,m ≥ 2, of class C0, the properties are studied of fields of ‘good directions’, that is the directions with respect to which ∂Ω can be locally represented as the graph of a continuous function. For any such domain there is a canonical smooth field of good directions defined in a suitable neighbourhood of ∂Ω, in terms of which a corresponding flow can be defined. Using...

We find a quartic example of a smooth embedded negatively curved surface in R homeomorphic to a doubly punctured torus. This constitutes an explicit solution to Hadamard’s problem on constructing complete surfaces with negative curvature and Euler characteristic in R. Further we show that our solution has the optimal degree of algebraic complexity via a topological classification for smooth cub...

We compute the Euler-Poincaré characteristic of quotients of the Bruhat-Tits building of PGL(n) under the action of arithmetic groups arising from central division algebras over rational function fields of positive characteristic. We use this result to determine the structure of the quotient simplicial complex in certain cases.

The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodge-theoretic invariants of algebraic varieties were announced by the first and third authors in [4, 11].

The generating function for Sn-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus g ≥ 2 is calculated. This answer generalizes the known ones for genera 2 and 3 and answers obtained by J. Bergstrom for any genus and n ≤ 7 points.

The Euler characteristic, thought of as a function that assigns a numerical value to every finite simplicial complex, is locally determined in both a combinatorial sense and a geometric sense. In this note we show that not every function that assigns a numerical value to every finite simplicial complex via a linear combination of the numbers of simplices in each dimension is locally determined ...

We show how to calculate the Euler characteristic of an affine Jacobi variety of a spectral curve from its defining equations. 0 Membre du CNRS 1 Laboratoire associé au CNRS.

We consider properly immersed finite topology minimal surfaces Σ in complete finite volume hyperbolic 3-manifolds N , and in M × S, where M is a complete hyperbolic surface of finite area. We prove Σ has finite total curvature equal to 2π times the Euler characteristic χ(Σ) of Σ, and we describe the geometry of the ends of Σ. .

Let us try to embed a graph 1, not necessarily simple, in a surface so that every odd polygon (the graph of a simple closed path of odd length), regarded as a path in the surface, reverses orientation while every even polygon preserves it. What is the smallest surface in which this is possible? That is, what is the minimum demigenus d(S)=2&/(S) over all embedding surfaces S? We call this kind o...

In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each n ≥ 3 we construct 4-manifolds E admitting at least n distinct fiberings pi : E → Σgi as a surface bundle over a surface with base and fiber both closed surfaces of negative Euler characteristic. We give examples of surface bundles admitting multiple fiberings for which th...