Localization Formulae in odd K-theory

Doctoral Dissertation

Abstract

We describe a class of real Banach manifolds, which classify $K^{-1}$. These manifolds are Grassmannians of (hermitian) lagrangian subspaces in a complex Hilbert space. Certain finite codimensional real subvarieties described by incidence relations define geometric representatives for the generators of the cohomology rings of these classifying spaces. Any family of self-adjoint, Fredholm operators parametrized by a closed manifold comes with a map to one of these spaces. We use these Schubert varieties to describe the Poincare duals of the pull-backs to the parameter space of the cohomology ring generators. The class corresponding to the first generator is the spectral flow.

Attributes

Attribute NameValues
URN
  • etd-03232009-095900

Author Florentiu Daniel Cibotaru
Advisor Bruce Williams
Contributor Liviu Nicolaescu, Committee Member
Contributor Stephan Stolz, Committee Member
Contributor Bruce Williams, Committee Member
Contributor Richard Hind, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2009-04-03

Submission Date 2009-03-23
Country
  • United States of America

Subject
  • index theory

  • spectral flow

  • K-theory

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

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