Related papers: Computing characteristic numbers using fixed point…

In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…

Let G be a semi-simple algebraic group over the complex numbers, B a Borel subgroup of G, T a maximal torus in B and P a parabolic in G containing B. This paper deals with singularities of T-stable subvarieties of G/P. It turns out that…

Let G be a semisimple algebraic Lie group and H a reductive subgroup. We find geometrically the best even integer p for which the representation of G in L^2(G/H) is almost L^{p}. As an application, we give a criterion which detects whether…

We consider a family of tight contact structures on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show some algebraic equivariant…

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…

We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…

Computation of the K- and KO-theory for the classifying G-spaces for proper actions of certain infinite discrete groups G via a special version of the equivariant Atiyah- Hirzebruch spectral sequence.

We describe new arithmetic invariants for pairs of torus orbits on groups isogenous to an inner form of $\mathbf{PGL}_n$ over a number field. These invariants are constructed by studying the double quotient of a linear algebraic group by a…

The classification of compact homogeneous spaces of the form $M=G/K$, where $G$ is a non-simple Lie group, such that the standard metric is Einstein is still open. The only known examples are $4$ infinite families and $3$ isolated spaces…

We identify the cotangent bundle Lie algebroid of a Poisson homogeneous space G/H of a Poisson Lie group G as a quotient of a transformation Lie algebroid over G. As applications, we describe the modular vector fields of G/H, and we…

Let G/H be a strongly regular homogeneous space such that H is a Lie group of inner type. We show that G/H admits a proper action of a discrete non-virtually abelian subgroup of G if and only if G/H admits a proper action of a subgroup L of…

Let $E$ be the bundle defined by applying a polynomial representation of $GL_n$ to the tautological bundle on the Hilbert scheme of $n$ points in the complex plane. By a result of Haiman, the Cech cohomology groups $H^i(E)$ vanish for all…

Let X be a homogeneous space of a connected linear algebraic group G' over a number field k, containing a k-point x. Assume that the stabilizer of x in G' is connected. Using the notion of a quasi-trivial group, recently introduced by…

Let $K$ be a global field of positive characteristic. We prove that the Brauer-Manin obstructions to the Hasse principle, to weak approximation and to strong approximation are the only ones for homogeneous spaces of reductive groups with…

Let K be a connected Lie group of compact type and let T*(K) be its cotangent bundle. This paper considers geometric quantization of T*(K), first using the vertical polarization and then using a natural Kahler polarization obtained by…

Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact Lie group…

Let $G$ be a (non compact) connected simply connected locally compact second countable Lie group, either abelian or unimodular of type I, and $\rho$ an irreducible unitary representation of $G$. Then, we define the analytic torsion of $G$…

Let a compact torus $T=T^{n-1}$ act on an orientable smooth compact manifold $X=X^{2n}$ effectively, with nonempty finite set of fixed points, and suppose that stabilizers of all points are connected. If $H^{odd}(X)=0$ and the weights of…

Consider a smooth irreducible Hodge generic curve $S$ defined over $\bar{\Q}$ in the Torelli locus $T_g\subset \mathcal{A}_g$. We establish Zilber-Pink-type statements for such curves depending on their intersection with the boundary of the…

We develop different formulas of algebraic and/or arithmetic nature allowing an explicit calculation, both over a finite field and over a field of characteristic 0, of the algebraic part of the unramified Brauer group of a homogeneous space…