Homological Calculations with the Analytic Structure Group

Open Access
Author:
Siegel, Paul Wilke
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
September 20, 2012
Committee Members:
  • John Roe, Dissertation Advisor
  • Dmitri Yu Burago, Committee Member
  • Nigel David Higson, Committee Member
  • Sean Hallgren, Committee Member
Keywords:
  • K-theory
  • Index Theory
  • Topology
  • Geometry
Abstract:
We build a Mayer-Vietoris sequence for the analytic structure group defined by Higson and Roe and use it to give a new proof of and generalizations of Roe’s partitioned manifold index theorem. We give applications of the generalized partitioned manifold index theorem to the theory of positive scalar curvature invariants. Finally, we construct an analogue of the Kasparov product for the analytic structure group and examine how positive scalar curvature invariants behave with respect to this product.