Foliations and exotic index theory

With regards to certain complete Riemannian manifolds we show that the analytic assembly map is rationally injective by using the exotic index theorem. The foliation exotic index theorem of S. Hurder is an extension of the theorem of G. Yu to the index theory for the foliations. Using the functorial property of the Kasparov KK-product, the foliation exotic index theorem can be recovered via the connecting homomorphism of K-homology theory. In the case of Riemannian foliations on compact manifolds, the corona of the holonomy groupoid is a fiber bundle over the ambient manifold whose fiber is the corona of the universal leaf. By this property, an idea in the work of S. Hurder can be applied to Riemannian foliations on a compact manifold to show that the analytic assembly map for foliations is rationally injective for certain Riemannian foliations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Kim, Eunsang

Contributors dc:contributor

• Kamber, Franz W.

• Mathematics

Statement dc:rights

• Copyright 1996 Kim, Eunsang

Language dc:language

eng

Identifier

9780591088021
AAI9702559
(UMI)AAI9702559

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23702