Connective 1-dimensional euclidean field theories

Doctoral Dissertation

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.

Attributes

Attribute NameValues
URN
  • etd-07122005-151903

Author Elke Katrin Markert
Advisor Stephan Stolz
Contributor Stephan Stolz, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2005-05-13

Submission Date 2005-07-12
Country
  • United States of America

Subject
  • connective ko-theory

  • field theories

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

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