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Type of Document Dissertation Author Markert, Elke Katrin URN etd-07122005-151903 Title Connective 1-dimensional euclidean field theories Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Stephan Stolz Committee Member Keywords
- connective ko-theory
- field theories
Date of Defense 2005-05-13 Availability unrestricted Abstract In this dissertation we construct an Omega-spectrum from spaces of certain supersymmetric one-dimensional euclidean field theories of degree n, which is a new model for connective ko-theory. The spaces of this spectrum form connective covers of the spaces of euclidean field theories constructed by S. Stolz and P. Teichner in their expository paper "What is an elliptic object?". We provide a direct proof of the loop spectrum properties and the connectivity using a quasi-fibration with contractible total space. This is at the same time a proof of Bott periodicity for the field theory model of K-theory and gives a description of the Bott element. We give an interpretation of one-dimensional euclidean field theories as configurations and make use of the convenient properties of configuration spaces to show the quasi-fibration properties. This connects our model of connective ko-theory to an older description due to G. Segal. Based on our result in the one-dimensional case, we give a conjecture for a connective version of spaces of two-dimensional conformal field theories. The ideas developed in this work might also help to prove the spectrum properties for the original spaces of conformal field theories of S. Stolz and P. Teichner, which is still an open problem.
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