topological phases of matter via K-theory -- references

Topological phases of matter via K-theory


Classification topological phases of matter (condensed matter with gapped Hamiltonians, topological insulators) by twisted equivariant topological K-theory:

Via cobordism cohomology:

Relation to the GSO projection:

For quasicrystals via KK-theory of the noncommutative topology of quasiperiodicity:


Under AdS/CFT duality in solid state physics the K-theory-classification of topological phases of matter translates to the K-Theory classification of D-brane charge in string theory, allowing a dual description of the topological phases even at strong coupling via AdS/CFT duality:

Relation to Yang-Mills monopoles as Dp/D(p+2)-brane intersections and Yang-Mills instantons as Dp/D(p+4)-brane intersections: