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## Details

Material Type: | Document, Thesis/dissertation, Internet resource |
---|---|

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Anssi Sebastian Lahtinen; Ralph L Cohen; G Carlsson; Søren Galatius; Stanford University. Department of Mathematics. |

OCLC Number: | 665198337 |

Notes: | Submitted to the Department of Mathematics. |

Description: | 1 online resource |

Responsibility: | Anssi Sebastian Lahtinen. |

### Abstract:

The mathematics in this thesis is motivated by the desire to connect the twisted equivariant K-theory of a compact Lie group G to the string topology of its classifying space BG. The thesis consists of two parts. In the first part, we prove a generalization of the Atiyah--Segal completion theorem to twisted K-theory, a result which Kriz, Westerland and Levin have subsequently used to connect the twisted equivariant K-groups of G to the Gruher--Salvatore string topology of BG. In the second part, we present work towards the construction of a conjectural family of field theories which, on one hand, are closely related to Freed, Hopkins and Teleman's field theories featuring the twisted equivariant K-theory of G, and which on the other hand contain the Chataur--Menichi string topology of BG as a special case. The main result of the second part is the construction of the field-theory operation associated with a fixed cobordism.

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