Frame bundle

About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.

Bundles of C*-categories and duality

Abstract: We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of C*-categories, with base space the spectrum of the C*-algebra associated with the identity object. We classify tensor C*-categories with fibre the dual of a compact Lie group in terms of suitable principal bundles. This also provides a classification for certain C*-algebra bundles, with fibres fixed-point algebras of O_d.

The $b$-boundary of tensor bundles over a space-time

Abstract: In [1] it was shown how to attach a boundary to any space-time. In the present paper a boundary is constructed for any bundle associated with the frame bundle of a space time. In such a way limits of tensor fields at boundary points of a space-time are defined. Using this we show that the Lorentz metric has always a unique continuous extension to theb-boundary of the space-time.

Parametrized Borsuk-Ulam problem for projective space bundles

Abstract: Let $\pi: E \to B$ be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let $\pi^{'}: E^{'} \to B$ be vector bundle such that $\mathbb{Z}_2$ acts fiber preserving and freely on $E$ and $E^{'}-0$, where 0 stands for the zero section of the bundle $\pi^{'}:E^{'} \to B$. For a fiber preserving $\mathbb{Z}_2$-equivariant map $f:E \to E^{'}$, we estimate the cohomological dimension of the zero set $Z_f = \{x \in E | f(x)= 0\}.$ As an application, we also estimate the cohomological dimension of the $\mathbb{Z}_2$-coincidence set $A_f=\{x \in E | f(x) = f(T(x)) \}$ of a fiber preserving map $f:E \to E^{'}$.

A Note on Vanishing Theorems

Abstract: On a Riemannian manifold we define a one-parameter family of Laplacians acting on sections of any bundle associated to the principal frame bundle via a representation, and show how various examples fit into this framework.