The Moduli Space of Compact Fiber Bundle Structures on a Fibration

Doctoral Dissertation

Abstract

Suppose that p is a fibration with total space E over a connected, finite CW complex B whose fibers are homotopy equivalent to a finite CW complex F. Then there is a fibration associated to p whose fibers are all homotopy equivalent to A(F), the algebraic K-theory space of F. Dwyer, Weiss, and Williams have constructed a section of this fibration, called the parametrized Euler characteristic of p, which has a lift to a parametrized excisive Euler characteristic if and only if p is fiber homotopy equivalent to a topological fiber bundle whose fibers are homeomorphic to a compact topological manifold, possibly with boundary.

Assuming that p does admit at least one compact topological fiber bundle structure, we can also try to classify the space of all such structures on p. We show that this space of structures on p is homotopy equivalent to the product of the space of all lifts of the parametrized Euler characteristic of p to a parametrized excisive Euler characteristic with the space of stable Euclidean bundles over E.

Attributes

Attribute NameValues
URN
  • etd-04162009-231731

Author Stacy Lynn Hoehn
Advisor E. Bruce Williams
Contributor E. Bruce Williams, Committee Chair
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2009-04-09

Submission Date 2009-04-16
Country
  • United States of America

Subject
  • algebraic K-theory

  • fiber bundles

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

Files

Please Note: You may encounter a delay before a download begins. Large or infrequently accessed files can take several minutes to retrieve from our archival storage system.