nLab Bott element

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 $1 - L \,\in\, K\big( \mathbb{C}P^1 \big)$ 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

• fundamental product theorem in topological K-theory

• equivariant K-theory of projective G-space.

Related entries

• Bott periodicity

References

• A Survey of Elliptic Cohomology - cohomology theories