nLab
Bott element

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

A Bott element is an element in a periodic cohomology theory, multiplication by which is invertible.

Specifically for complex topological K-theory there is the element of 1LK(P 1)1 - L \,\in\, K\big( \mathbb{C}P^1 \big) degree 2 (the virtual difference of the trivial line bundle with the tautological line bundle on the Riemann sphere/complex projective 1-space) which induces Bott periodicity. This is where the term “Bott element” comes from. For details on this case see at

References

Last revised on November 12, 2020 at 07:14:31. See the history of this page for a list of all contributions to it.