nLab stable tangent bundle




By the stable tangent bundle of a smooth manifold one means the Whitney sum of the actual tangent bundle with any trivial vector bundle.

Specifically, for {G k} k\{G_k\}_{k \in \mathbb{N}} a sequence of Lie groups, a “G-structure on the stable tangent bundle” is an actual Gk-structure on any such direct sum TX̲ nT X \oplus \underline{\mathbb{R}}^n, for some nn \in \mathbb{N}.

In particular, for G=1G = 1 the trivial group, a stable framing? is a trivialization of the stable tangent bundle.


Last revised on December 3, 2020 at 19:36:54. See the history of this page for a list of all contributions to it.