ﻻ يوجد ملخص باللغة العربية
Let $Gamma$ be a finitely generated group and let $(X,mu_X)$ be an ergodic standard Borel probability $Gamma$-space. Suppose that $G$ is the connected component of the identity of the isometry group of a Hermitian symmetric space. Given a Zariski dense measurable cocycle $sigma:Gammatimes Xrightarrow G$, we define the notion of parametrized K{a}hler class and we show that it completely determines the cocycle up to cohomology.
We extend Ghys theory about semiconjugacy to the world of measurable cocycles. More precisely, given a measurable cocycle with values into $text{Homeo}^+(mathbb{S}^1)$, we can construct a $text{L}^infty$-parametrized Euler class in bounded cohomology
Primary cohomology operations, i.e., elements of the Steenrod algebra, are given by homotopy classes of maps between Eilenberg--MacLane spectra. Such maps (before taking homotopy classes) form the topological version of the Steenrod algebra. Composit
Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus. This
It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we construct nontrivial homomorphisms from infinite-genus mapping class groups
We study the space of nearly K{a}hler structures on compact 6-dimensional manifolds. In particular, we prove that the space of infinitesimal deformations of a strictly nearly K{a}hler structure (with scalar curvature scal) modulo the group of diffeom