Approximation property of C*-algebraic bundles

A COVERING PROPERTY IN PRINCIPAL BUNDLES

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

Vector bundles over algebraic curves

Representations of Algebraic Groups and Principal Bundles on Algebraic Varieties

In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic p. We quickly review the notions of stable and semistable vector bundles and principal G-bundles , where G is any semisimple group. We define the notion of a low height representation in characteristic p and outline a proof of the theorem t...

Algebraic Property Testing

Modern computational tasks often involve large amounts of data, and efficiency is a very desirable feature of such algorithms. Local algorithms are especially attractive, since they can imply global properties by only inspecting a small window into the data. In Property Testing, a local algorithm should perform the task of distinguishing objects satisfying a given property from objects that req...

The Strong Approximation Property and the Weak Bounded Approximation Property

We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja’s conjecture. As a consequence, we show that each of the spaces c0 and `1 has a subspace which has the AP but fails to have the strong AP.