Related papers: Euler characteristics of centralizer subcategories

Let $N$ be normal subgroup of a finite group $G$, $p$ be a prime, $P$ be a Sylow $p$-subgroup of $G$ and $\theta$ be a $P$-invariant irreducible character of $N$. Suppose that $G/N$ is a $p$-solvable group. In this note we show that,…

If A is an Abelian variety, endowed with a polarization L, we study the function N_A(t) which counts the number of Abelian subvarieties S in A such that for the induced polarization L|_S the Euler characteristic \chi(L|_S) is bounded above…

We determine all the equivariant Euler characteristics of the building for the general unitary group over a finite field.

Let A be the path algebra of a quiver Q with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given A-module M. In particular, we obtain some sufficient conditions for smoothness, polynomial…

We prove an analog of the Gauss-Bonnet formula for constructible sheaves on reductive groups. As a corollary from this formula we get that if a perverse sheaf on a reductive group is equivariant under the adjoint action, then its Euler…

We write the Euler characteristic X(G) of a four dimensional finite simple geometric graph G=(V,E) in terms of the Euler characteristic X(G(w)) of two-dimensional geometric subgraphs G(w). The Euler curvature K(x) of a four dimensional…

Let $\mathcal{A}$ be a Weyl arrangement. We introduce and study the notion of $\mathcal{A}$-Eulerian polynomial producing an Eulerian-like polynomial for any subarrangement of $\mathcal{A}$. This polynomial together with shift operator…

Eggert's Conjecture says that if R is a finite-dimensional nilpotent commutative algebra over a perfect field F of characteristic p, and R^{(p)} is the image of the p-th power map on R, then dim_F R \geq p dim_F R^{(p)}. Whether this very…

Let $G$ be a unimodular locally compact group. We define a property of irreducible unitary $G$-representations $V$ which we call c-temperedness, and which for the trivial $V$ boils down to F{\o}lner's condition (equivalent to the trivial…

We prove the $L^2$-Euler characteristic has the invariance under the barycentric subdivision only for finite acyclic categories. And we extend the definition of $L^2$-Euler characteristic and prove the extended $L^2$-Euler characteristic…

The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here…

The Euler discriminant of a family of very affine varieties is defined as the locus where the Euler characteristic drops. In this work, we study the Euler discriminant of families of complements of hyperplanes. We prove that the Euler…

We define a bicomplex whose Euler characteristic is the idempotented version of the ribbon element of quantum sl(2). We show that properties of this bicomplex descend to the centrality, invertibility and symmetries of the ribbon element…

We define and study a bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot Floer homology. The invariant is the homology of a chain complex whose generators correspond to Kauffman states…

We define a partial order $\mathcal{P}_n$ on permutations of any given size $n$, which is the image of a natural partial order on inversion sequences. We call this the ``middle order''. We demonstrate that the poset $\mathcal{P}_n$ refines…

We apply the Atiyah-Singer index theorem and tensor products of elliptic complexes to the cohomology of transitive Lie algebroids. We prove that the Euler characteristic of a representation of a transitive Lie algebroid $A$ over a compact…

The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds,…

Let k be an algebraically closed field of positive characteristic and G a simple algebraic group defined over k. Under the assumption that the characteristic is a good prime for G, we determine a maximal G-stable subvariety U' of the…

We extend the Euler's totient function (from arithmetic) to any irreducible subfactor planar algebra, using the Mobius function of its biprojection lattice, as Hall did for the finite groups. We prove that if it is nonzero then there is a…

The weights for a finite group G with respect to a prime number p where introduced by Jon Alperin, in order to formulate his celebrated conjecture affirming that that the number of G-conjugacy classes of weights of G coincides with the…