nLab twisted equivariant differential K-theory




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

  1. twisted K-theory

  2. equivariant K-theory

  3. differential K-theory

hence the joint generalization of

  1. twisted equivariant K-theory

  2. twisted differential K-theory

  3. equivariant differential K-theory.

It is this joint generalization that is, ultimately, required by

  1. the K-theory classification of D-brane charge,

    conjectured to apply to non-perturbative type II string theory;

  2. 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.