group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
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
Last revised on November 12, 2020 at 12:14:31. See the history of this page for a list of all contributions to it.