Stabilization and classification of poincare duality embeddings

<p>We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.</p> <p>This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In</p> <p>particular, a Poincare embedding gives rise to a fiberwise duality</p> <p>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</p> <p>smooth embeddings.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2012

Author dc:creator

• Peter, John Whitson

Contributors dc:contributor

• John R. Klein

• Mathematics

Repository record dc:identifier

https://digitalcommons.wayne.edu/oa_dissertations/470

OAI identifier oai:identifier

oai:digitalcommons.wayne.edu:oa_dissertations-1469