We show that Preissmann’s theorem implies that no closed negatively curved manifold is dominated by a non-trivial product. We also show that a fiber bundle whose base and fiber are negatively curved is dominated by a product if and only if it has a finite covering space which is a trivial bundle.

Our main result states that given a finitely generated subgroup G of Aut(CP (2)), there is an algebraic foliation F on a complex projective 3-manifold M3 with a bundle structure over CP (1) and fiber CP (2), such that F is transverse to almost every fiber of the bundle and with global holonomy conjugate to G.

We prove that the mathematical framework for the de Sitter top system is the de Sitter fiber bundle. In this context, the concept of soldering associated with a fiber bundle plays a central role. We comment on the possibility that our formalism may be of particular interest in different contexts including MacDowell-Mansouri theory, two time physics and oriented matroid theory.

The statistical properties of failure are studied in a fiber bundle model with thermal noise. We find that in agreement with recent experiments the macroscopic failure is produced by a thermal activation of microcracks. Most importantly the effective temperature of the system is amplified by the spatial disorder (heterogeneity) of the fiber bundle.

Let η = (E, p, Y, F, K) be a locally definable fiber bundle and f, h : X → Y two locally definable maps. If f and h are locally definably homotopic, then f ∗(η) and h∗(η) are locally definably fiber bundle isomorphic. 2000 Mathematics Subject Classification. 14P10, 14P20, 03C64.

We prove that the mathematical framework for the de Sitter top system is the de Sitter fiber bundle. In this context, the concept of soldering associated with a fiber bundle plays a central role. We comment on the possibility that our formalism may be of particular interest in different contexts including MacDowell-Mansouri theory, two time physics and oriented matroid theory.

A Riemann-Roch theorem asserts that some algebraically defined wrong– way map in K-theory agrees with a topologically defined one [BFM]. Bismut and Lott [BiLo] proved a Riemann–Roch theorem for smooth fiber bundles in which the topologically defined wrong–way map is the homotopy transfer of Becker–Gottlieb and Dold. We generalize their theorem, refine it, and prove a converse stating that an ap...

For the class of fibrations which admit a reduction to a fiber bundle with compact topological manifold fibers, Becker and Schultz showed that the Becker-Gottlieb transfer is uniquely characterized by four axioms. In this paper, we consider a refinement of the transfer, also described by Becker and Gottlieb. We show that a version of the Becker-Schultz axioms uniquely determines the refined tra...

Riemann-Roch theorems assert that certain algebraically defined wrong way maps (transfers) in algebraic K–theory agree with topologically defined ones [BaDo]. Bismut and Lott [BiLo] proved such a Riemann–Roch theorem where the wrong way maps are induced by the projection of a smooth fiber bundle, and the topologically defined transfer map is the Becker–Gottlieb transfer. We generalize and refin...

Let π : P → B be a locally trivial fiber bundle over a connected CW complex B with fiber equal to the closed symplectic manifold (M,ω). Then π is said to be a symplectic fiber bundle if its structural group is the group of symplectomorphisms Symp(M,ω), and is called Hamiltonian if this group may be reduced to the group Ham(M,ω) of Hamiltonian symplectomorphisms. In this paper, building on prior...