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String topology and twisted K-theory

Author: Anssi Sebastian Lahtinen; Ralph L Cohen; G Carlsson; Søren Galatius; Stanford University. Department of Mathematics.
Publisher: 2010.
Dissertation: Thesis (Ph. D.)--Stanford University, 2010.
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
Summary:
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  Read more...
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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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