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https://hdl.handle.net/2142/23702
Description
Title
Foliations and exotic index theory
Author(s)
Kim, Eunsang
Issue Date
1996
Doctoral Committee Chair(s)
Kamber, Franz W.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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