Related papers: Cocycle Rigidity and Splitting for some Discrete P…

In this paper we study the variability and rigidity of secondary characteristic classes which arise from flat connections on a manifold. Considering the connection as a Lie-algebra valued one-form, we study the characteristic map from Lie…

We show the local rigidity of the natural action of the Borel subgroup of SO_+(n,1) on a cocompact quotient of SO_+(n,1) for n>2.

In this paper, we present a generalisation of a theorem of David and Rob Pollack. In 'A construction of rigid analytic cohomology classes for congruence subgroups of SL(3,Z)', they give a very general argument for lifting ordinary…

Let $d \geq 2$, and let $\Gamma \subset PSL(2, \mathbb{R})^d$ be an irreducible, cocompact lattice. We prove a sharp estimate up to a logarithmic factor on the rate of equidistribution of coordinate horocycle flows on $\Gamma \backslash…

We investigate the first two Galois cohomology groups of $p$-extensions over a base field which does not necessarily contain a primitive $p$th root of unity. We use twisted coefficients in a systematic way. We describe field extensions…

We define a cohomology for an arbitrary $K$-linear semistrict semigroupal 2-category $(\mathfrak{C},\otimes)$ (called in the paper a Gray semigroup) and show that its first order (unitary) deformations, up to the suitable notion of…

When $X=\Gamma\backslash \H^n$ is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of $L^2$ harmonic forms vanish. In this paper, we show rigidity…

Let $\mathbb{F}_{\Theta }=G/P_{\Theta }$ be a flag manifold associated to a non-compact real simple Lie group $G$ and the parabolic subgroup $% P_{\Theta }$. This is a closed subgroup of $G$ determined by a subset $% \Theta $ of simple…

We discuss `hd-compactifications' of $\SL(2,\bbK)$ for $\bbK=\bbC$ or $\bbR.$ These are compact manifolds with boundary on which both the Schwartz and the Harish-Chandra Schwartz spaces are shown to be relatively standard spaces of conormal…

We give a simple proof about the topological rigidity of closures of certain sparse unipotent orbits in $G/\Gamma$ where $G=\prod_{i=1}^k\operatorname{SL}_2(\mathbb R)$ and $\Gamma$ is an irreducible lattice in $G$.

We extend the computations in our prior work to find the cohomology in degree five of a congruence subgroup Gamma of SL_4(Z) with coefficients in Sym^g(K^4), twisted by a nebentype character eta, along with the action of the Hecke algebra.…

We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes restricting…

Given a discrete subgroup $\Gamma$ of finite co-volume of $\mathrm{PGL}(2,\mathbb{R})$, we define and study parabolic vector bundles on the quotient $\Sigma$ of the (extended) hyperbolic plane by $\Gamma$. If $\Gamma$ contains an…

We introduce a graph-theoretical interpretation of an induced action of Aut$(\Gamma)$ in the discrete de Rham cohomology of a finite graph $\Gamma$. This action produces a splitting of Aut$(\Gamma)$ that depends on the cycles of $\Gamma$.…

Using techniques developed in a recent article by the authors, it is proved that the 2-cohomology of the Lie superalgebra sl(m|1); m > 1, with coefficients in its enveloping algebra is trivial. The obstacles in solving the analogous problem…

Finite rank median spaces are a simultaneous generalisation of finite dimensional ${\rm CAT}(0)$ cube complexes and real trees. If $\Gamma$ is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of…

An unexpected behavior of pure septic fields L = Q(D^1/7) with certain prime radicands D congruent to 2 or 4 modulo 7, which split in the cyclotomic field of seventh roots of unity, is proved by direct computation. Whereas the Galois…

Consider a proper action of $\mathbb{Z}^d$ on a smooth (perhaps non-paracompact) manifold $M$. The $p^{th}$ cohomology $H^p(\mathbb{Z}^d,\ \Gamma_{\mathrm{c}}(\mathcal{F}))$ valued in the space of compactly-supported sections of a natural…

We show that the cohomology of the structure sheaf of smooth and proper schemes over a complete non-archimedean field $K$ of characteristic zero, can be refined to an $\mathbf{A}^1$-invariant cohomology theory of smooth (not necessarily…

Let $G$ be a semisimple Lie group acting on a space $X$, let $\mu$ be a compactly supported measure on $G$, and let $A$ be a strongly irreducible linear cocycle over the action of $G$. We then have a random walk on $X$, and let $T$ be the…