Fixed points on trivial surface bundles over a connected CW-complex

Nonexpansive mappings on complex C*-algebras and their fixed points

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...

Ordered abelian groups over a CW complex

If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by EX . In the present work we establish a topological classification of such bundles in terms of the first cohomology group of X with coefficients in the ring Z2.

Locally trivial W∗-bundles

Atoroidal surface bundles over surfaces

The main aim of this paper is to prove a finiteness result for atoroidal surface bundles over surfaces. It can be viewed from a number of different perspectives, and one can give several essentially equivalent statements. This, and related questions, have been considered by a number of authors. See [R] for a recent survey. First, we express it in group theoretical terms. By a surface group we m...

On Semistable Principal Bundles over a Complex Projective Manifold, Ii

Let (X, ω) be a compact connected Kähler manifold of complex dimension d and EG −→ X a holomorphic principal G–bundle, where G is a connected reductive linear algebraic group defined over C. Let Z(G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P ⊂ G and a holomorphic reduction of structure group EP ⊂ EG to P , such that ...