相关论文: Exotic symmetric space over a finite field, II

For having a Poincar\'e duality via a cap product between the intersection homology of a paracompact oriented pseudomanifold and the cohomology given by the dual complex, G. Friedman and J. E. McClure need a coefficient field or an…

We argue that extremal black holes of N=4 Poincare supergravity coupled to conformal matter have a quantum-exact dual 5-d description in the maximally supersymmetric extension of the Randall-Sundrum theory. This dual is a the classical,…

We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the…

We construct series of examples of exotic smooth structures on compact locally symmetric spaces of noncompact type. In particular, we obtain higher rank examples, which do not support Riemannian metric of nonpositive curvature. The examples…

It is well-known that the Thom polynomial in Stiefel--Whitney classes expressing the cohomology class dual to the locus of the cusp singularity for codimension-$k$ maps and that of the corank-$2$ singularity for codimension-$(k-1)$ maps…

When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…

Equivariant localization expresses global invariants in terms of local invariants, and many of them appearing in equivariant index theory, (holomorphic) Morse theory, geometric quantization and supersymmetric localization can be…

We study the numerical characterization of two dimensional hard Lefschetz classes given by the complete intersections of nef classes. In Shenfeld and van Handel's breakthrough work on the characterization of the extremals of the…

Given a decomposition of a vector space $V=V_1\oplus V_2$, the direct product $\mathfrak{X}$ of the projective space $\mathbb{P}(V_1)$ with a Grassmann variety $\mathrm{Gr}_k(V)$ can be viewed as a double flag variety for the symmetric pair…

The paper contains the proof, in dimension 2, of a conjecture of R. G. Douglas and V. Paulsen concerning the characterization of the ideals of polynomials which are closed in the relative topology induced by the Hardy space of the polydisk.

In our previous work [H. Zejli, Int. J. Mod. Phys. D 34, 2550052 (2025), arXiv:2508.00035], we introduced a PT-symmetric wormhole model based on a bimetric geometry, capable of generating closed timelike curves (CTCs). In this paper, we…

We discover a new Poincar\'e type phenomenon by establishing an optimal rigidity theorem for local CR mappings between circle bundles that are defined in a canonical way over (possibly reducible) bounded symmetric domains. We prove such a…

Theory of motivic superpolynomials is developed, including its extension to algebraic links colored by rows, relations to $L$-functions of plane curve singularities, the justification of the motivic versions of Weak Riemann Hypothesis, and…

We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separation of variables in Cartesian coordinates and hence allow a…

We present the consistent approach to finding the discrete transformations in the representation spaces of the proper Poincar\'e group. To this end we use the possibility to establish a correspondence between involutory automorphisms of the…

We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology…

In [5] I.P. Goulden, D.M. Jackson, and R. Vakil formulated a conjecture relating certain Hurwitz numbers (enumerating ramified coverings of the sphere) to the intersection theory on a conjectural Picard variety. We are going to use their…

We show that the exterior algebra $\Lambda_{R}\left[\alpha_{1}, \cdots, \alpha_{n}\right]$, which is the cohomology of the torus $T=(S^{1})^{n}$, and the polynomial ring $\mathbb{R}\left[t_{1}, \ldots, t_{n}\right]$, which is the cohomology…

We improve the known Hodge type bound for the exotic cohomology of complete intersections. In the revised version, we included a simplification of our original argument due to Pierre Deligne. The note appears in the C. R. de l'Aca. des Sc.…

In this paper, we proved that for a bounded Hopf-symmetric domain $\Omega$ in a noncompact rank one symmetric space $M$, the second Dirichlet eigenvalue $\lambda_2 (\Omega) \leq \lambda_2 (B_1)$ where $B_1$ is a geodesic ball in $M$ such…