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.
|Author||Elke Katrin Markert|
|Contributor||Stephan Stolz, Committee Member|
|Degree Level||Doctoral Dissertation|
|Departments and Units|