String topology and twisted K-theory

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Abstract/Contents

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.

Type of resource	text
Form	electronic; electronic resource; remote
Extent	1 online resource.
Publication date	2010
Issuance	monographic
Language	English

Associated with	Lahtinen, Anssi Sebastian
Associated with	Stanford University, Department of Mathematics
Primary advisor	Cohen, Ralph L, 1952-
Thesis advisor	Cohen, Ralph L, 1952-
Thesis advisor	Carlsson, G. (Gunnar), 1952-
Thesis advisor	Galatius, Søren, 1976-
Advisor	Carlsson, G. (Gunnar), 1952-
Advisor	Galatius, Søren, 1976-

Genre	Theses

Statement of responsibility	Anssi Lahtinen.
Note	Submitted to the Department of Mathematics.
Thesis	Thesis (Ph.D.)--Stanford University, 2010.
Location	electronic resource

License: This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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