The notion of twisted equivariant differential K-theory is meant to be the joint generalization of all three variations of topological K-theory given by
hence the joint generalization of
It is this joint generalization that is, ultimately, required by
the K-theory classification of D-brane charge,
conjectured to apply to non-perturbative type II string theory;
the K-theory classification of topological phases of matter,
conjectured to apply in topological condensed matter theory.
The construction of full twisted & equivariant & differential cohomology theories had long been left open. It does follow as an immediate consequence of the twisted & equivariant Chern-Dold character and as such is discussed in:
The twisted + equivariant + flat differential sector of K-theory is more readily described:
Last revised on May 11, 2022 at 19:19:44. See the history of this page for a list of all contributions to it.