Related papers: Euler Characteristic in Odd Dimensions

Manifolds all of whose geodesics are closed have been studied a lot, but there are only few examples known. The situation is different if one allows in addition for orbifold singularities. We show, nevertheless, that the abundance of new…

We compute the Euler characteristics of the recently discovered series of Gothic Teichm\"{u}ller curves. The main tool is the construction of 'Gothic' Hilbert modular forms vanishing at the images of these Teichm\"{u}ller curves. Contrary…

We prove that the mean Euler characteristic of a Gorenstein toric contact manifold, i.e. a good toric contact manifold with zero first Chern class, is equal to half the normalized volume of the corresponding toric diagram and give some…

This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae…

We provide a generating function for the (graded) dimensions of M. Kontsevich's graph complexes of ordinary graphs. This generating function can be used to compute the Euler characteristic in each loop order. Furthermore, we show that…

We generalize the notions of the orbifold Euler characteristic and of the higher order orbifold Euler characteristics to spaces with actions of a compact Lie group. This is made using the integration with respect to the Euler characteristic…

Let $(X,g)$ be a compact $n$-dimensional smooth Riemannian manifold with a lower bound on the average of the lowest $n-p$ eigenvalues of the curvature operator and the diameter of $X$ is bounded above by $D>0$. In this article, we…

A nontrivial smooth steady incompressible Euler flow in three dimensions with compact support is constructed. Another uncommon property of this solution is the dependence between the Bernoulli function and the pressure.

A perfect cuboid, popularly known as a perfect Euler brick/a perfect box, is a cuboid having integer side lengths, integer face diagonals and an integer space diagonal. Euler provided an example where only the body diagonal became deficient…

In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related…

Let $W$ be a Weyl group, and let $\CT_W$ be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of $W$, and its weight lattice. The real locus $\CT_W(\R)$ is a smooth, connected, compact…

In this short paper, we give two proofs that the Euler characteristic is multiplicative, for fiber sequences of finitely dominated spaces. This is equivalent to proving that the Becker-Gottlieb transfer is functorial on $\pi_0$.

We extend Auslander and Buchsbaum's Euler characteristic from the category of finitely generated modules of finite projective dimension to the category of modules of finite G-dimension using Avramov and Martsinkovsky's notion of relative…

We show that a compact manifold admitting a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex projective spaces, provided that the singular foliation defined by the closures of…

We introduce the universal Euler characteristic of orbit space definable groupoids, a class of groupoids containing cocompact proper Lie groupoids as well as translation groupoids associated to proper definable group actions. We show that…

This paper presents "oriented pivoting systems" as an abstract framework for complementary pivoting. It gives a unified simple proof that the endpoints of complementary pivoting paths have opposite sign. A special case are the Nash…

We prove that for n>4 there is no compact arithmetic hyperbolic n-manifold whose Euler characteristic has absolute value equal to 2. In particular, this shows the nonexistence of arithmetically defined hyperbolic rational homology n-sphere…

Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type…

We assign to a finite $CW$-complex and an element in its first cohomology group a twisted version of the $L^2$-Euler characteristic and study its main properties. In the case of an irreducible orientable $3$-manifold with empty or toroidal…

We prove Chern conjecture, which states that the Euler characteristic vanishes for closed flat affine manifolds. Our key innovation is a deformation argument for the Euler form.