Related papers: Higher Euler characteristics
We present several recent results concerning Cauchy and event horizons. In the first part of the paper we review the differentiablity properties of the Cauchy and the event horizons. In the second part we discuss compact Cauchy horizons and…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
Let G be a finite, complex reflection group and f its discriminant polynomial. The fibers of f admit commuting actions of G and a cyclic group. The virtual $G\times C_m$ character given by the Euler characteristic of the fiber is a…
In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. We introduce equivariant cohomology and equivariant formal deformation theory of Lie superalgebras. As an application of equivariant…
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…
We define a Grothendieck ring of varieties with finite groups actions and show that the orbifold Euler characteristic and the Euler characteristics of higher orders can be defined as homomorphisms from this ring to the ring of integers. We…
We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincar\'e duality.…
In this paper, we investigate geometric properties of some curvature tensors of a four-dimensional Walker manifold. Some characterization theorems are also obtained.
We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections;…
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae…
Recently there has been a renewed interest in asymptotic Euler-MacLaurin formulas, partly due to applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth…
The Euler characteristic of the link of a real algebraic variety is an interesting topological invariant in order to discuss local topological properties. We prove in the paper that an invariant stronger than the Euler Characteristic is…
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…
In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…
In this thesis, we study cohomological properties of non-K\"ahler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g.,…
The numbers of even and odd permutations with a given ascent number are investigated using an operator that was previously introduced by the author. Their difference is called a signed Eulerian number. By means of the operator the…
In this article, we develop a new index theory for noncompact manifolds endowed with an admissible exhaustion by compact sets. This index theory allows us to provide examples of noncompact manifolds with exotic positive scalar curvature…
In this paper, we introduce the hypergeometric Euler number as an analogue of the hypergeometric Bernoulli number and the hypergeometric Cauchy number. We study several expressions and sums of products of hypergeometric Euler numbers. We…
We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject only to the condition that the irreducible components of…
The Euler characteristic of a semialgebraic set can be considered as a generalization of the cardinality of a finite set. An advantage of semialgebraic sets is that we can define "negative sets" to be the sets with negative Euler…