nLab stable tangent bundle

Idea

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

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

Examples

• stable complex structure

• …

Related concepts

• stable normal bundle?

• cobordism theory