Related papers: Equivariant Euler characteristics of subspace pose…
We provide a natural interpretation of the secondary Euler characteristic and introduce higher Euler characteristics. For a compact oriented manifold of odd dimension, the secondary Euler characteristic recovers the Kervaire…
We give a formula for the Euler characteristic of a triangulated manifold of even dimension in terms of the numbers of even-dimensional faces only. The coefficients in this formula are universal (they do not depend on the dimension of the…
We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.
We find an algorithm to compute the quadratic Euler characteristic of a smooth projective complete intersection of hypersurfaces of the same degree. As an example, we compute the quadratic Euler characteristic of a smooth projective…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
In this paper we introduce and study the Euler characteristic associated with algebraic modules generated by arbitrary elements of certain noncommutative polyballs. We provide several asymptotic formulas and prove some of its basic…
We revisit Allendoerfer-Weil's formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, first taking some time to re-prove it while demonstrating techniques of [2] and then applying it to…
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative…
If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the…
If two G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers…
We relate certain universal curvature identities for Kaehler manifolds to the Euler-Lagrange equations of the scalar invariants which are defined by pairing characteristic forms with powers of the Kaehler form.
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…
We construct the odd symplectic structure and the equivariant even (pre)symplectic one from it on the space of differential forms on the Riemann manifold. The Poincare -- Cartan like invariants of the second structure define the equivariant…
We give explicit computations of the $\Gamma$-Euler characteristic of several families of orbit space definable translation groupoids. These include the translation groupoids associated to finite-dimensional linear representations of the…
We use some basic properties of binomial and Stirling numbers to prove that the Euler characteristic is, essentially, the unique numerical topological invariant for compact polyhedra which can be expressed as a linear combination of the…
We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown…
The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The…
In this short note we present a generating function computing the compactly supported Euler characteristic $\chi_c(F(X, n), K^{\boxtimes n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible…
We give a determination of the equivalence group of Euler-Bernoulli equation and of one of its generalizations, and thus derive some symmetry properties of this equation.
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.