KO-theory

The generalized cohomology theory represented by the KO-spectrum, hence the “orthogonal” version of complex K-theory.

**cohomology theories of string theory fields on orientifolds**

string theory | B-field | $B$-field moduli | RR-field |
---|---|---|---|

bosonic string | line 2-bundle | ordinary cohomology $H\mathbb{Z}^3$ | |

type II superstring | super line 2-bundle | $Pic(KU)//\mathbb{Z}_2$ | KR-theory $KR^\bullet$ |

type IIA superstring | super line 2-bundle | $B GL_1(KU)$ | KU-theory $KU^1$ |

type IIB superstring | super line 2-bundle | $B GL_1(KU)$ | KU-theory $KU^0$ |

type I superstring | super line 2-bundle | $Pic(KU)//\mathbb{Z}_2$ | KO-theory $KO$ |

type $\tilde I$ superstring | super line 2-bundle | $Pic(KU)//\mathbb{Z}_2$ | KSC-theory $KSC$ |

The differential K-theory for KO is discussed in

- Daniel Grady, Hisham Sati,
*Differential KO-theory: Constructions, computations, and applications*(arXiv:1809.07059)

Last revised on January 30, 2019 at 02:58:38. See the history of this page for a list of all contributions to it.