Related papers: Locally Trivial W*-Bundles

Guillet and Soul\'e have shown that, for a fibration $\pi: Y \to X$ with fibre $Z$, locally trivial in the Zariski topology, we have a decomposition \[ [Y] = [X] \cdot [Z], \] where $[\cdot]$ denotes a class in the Grothendieck group…

The potential global topological obstructions to the tetrad approach to finding the quasi-local conserved quantities, associated with closed, orientable spacelike 2-surfaces S, are investigated. First we show that the Lorentz frame bundle…

We address a number of problems concerning the (im)possibility of either extending locally trivial subbundles of possibly singular Banach/$C^*$ bundles globally, embedding subhomogeneous bundles into homogeneous ones, or recovering locally…

We prove that the Teichm\"uller space of the Hirsch foliation (a minimal foliation of a closed 3-manifold by non-compact hyperbolic surfaces) is homeomorphic to the space of closed curves in the plane. This allows us to show that that the…

Let $\Sigma$ be an orientbale closed surface and let $\Sigma'$ be a nonorientable closed surface. In the paper, we show that for any nontrivial orientable $S^2$ fiber bundles $X= \Sigma \ltimes S^2$ and $X' = \Sigma' \ltimes S^2$, there are…

Given an arbitrary topological complex vector space $A$, a quotient vector bundle for $A$ is a quotient of a trivial vector bundle $\pi_2:A\times X\to X$ by a fiberwise linear continuous open surjection. We show that this notion subsumes…

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 E(X).…

We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $\pi_1$ of the group is invertible in the ground field, or if the curve has semi-normal…

We study the relations between the triviality of the tangent bundle $TM$ and the generalized tangent bundle $\mathbb{T}M = TM\oplus T^*M$ of a manifold. We show that the generalized tangent bundle of a paralellizable manifold is trivial. We…

A space $X$ is called $W$-trivial if for every vector bundle $\xi$ over $X$, the total Stiefel-Whitney class $W(\xi)= 1$. In this article we shall investigate whether the suspensions of Dold manifolds, $\s^k D(m,n)$, is $W$-trivial or not.

Let R be a regular local ring, containing a finite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. If the regular local ring R contains an…

Let C $\rightarrow$ Spec(R) be a relative proper flat curve over an henselian base. Let G be a reductive C-group scheme. Under mild technical assumptions, we show that a G-torsor over C which is trivial on the closed fiber of C is locally…

We construct a locally compact groupoid with the properties in the title. Our example is based closely on constructions used by Higson, Lafforgue, and Skandalis in their work on counterexamples to the Baum-Connes conjecture. It is a bundle…

We study the ring of characteristic classes with values in the Chow ring for principal $G$-bundles over schemes. If we consider bundles which are locally trivial in the Zariski topology, then we show, for $G$ reductive, that this ring is…

We consider compact $CR$ manifolds of arbitrary $CR$ codimension that satisfy certain geometric conditions in terms of their Levi form. Over these compact $CR$ manifolds, we construct a deformation of the trivial $CR$ line bundle over $M$…

We give a classification of many closed Riemannian manifolds M whose universal cover possesses a nontrivial amount of symmetry. More precisely, we consider closed Riemannian manifolds $M$ such that Isom$(\widetilde{M})$ has noncompact…

Let $M$ be a compact connected complex manifold and $G$ a connected reductive complex affine algebraic group. Let $E_G$ be a holomorphic principal $G$--bundle over $M$ and $T\, \subset\, G$ a torus containing the connected component of the…

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.

Winkelmann considered compact complex manifolds $X$ equipped with a reduced effective normal crossing divisor $D\, \subset\, X$ such that the logarithmic tangent bundle $TX(-\log D)$ is holomorphically trivial. He characterized them as…

Let $X$ be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of $C(X)$-algebras by $C(X)$-subalgebras with controlled complexity. The following…