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Title:Foliations and exotic index theory
Author(s):Kim, Eunsang
Doctoral Committee Chair(s):Kamber, Franz W.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract: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.
Issue Date:1996
Type:Text
Language:English
URI:http://hdl.handle.net/2142/23702
ISBN:9780591088021
Rights Information:Copyright 1996 Kim, Eunsang
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9702559
OCLC Identifier:(UMI)AAI9702559


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