Access Type
Open Access Dissertation
Date of Award
January 2012
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
John R. Klein
Abstract
We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.
This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In
particular, a Poincare embedding gives rise to a fiberwise duality
map in the category of retractive spaces over X. We use this construction to obtain a highly connected classification map with target a moduli space of unstable complements for Poincare embeddings. As consequences, we obtain stabilization and classication results for
smooth embeddings.
Recommended Citation
Peter, John Whitson, "Stabilization and classification of poincare duality embeddings" (2012). Wayne State University Dissertations. 470.
https://digitalcommons.wayne.edu/oa_dissertations/470