SARTIPI-DISSERTATION-2019.pdf (635.41 kB)
Paschke Category, K-homology, and the Riemann-Roch Transformation
thesis
posted on 2019-08-01, 00:00 authored by Khashayar SartipiFor a separable C*-algebra A, We define an exact C*-category called the Paschke Category of A, and show that its topological K-theory groups are equal to topological K-homology groups of the C*-algebra A. Then we use the Dolbeault complex and ideas from the classical methods in Kasparov K-theory to construct an acyclic chain complex in this category, which in turn, induces a Riemann-Roch transformation from algebraic K-theory spectra of a complex manifold X, to its topological K-homology spectra. We examine the question of whether this map commutes with push-forward with respect to a proper map of complex manifolds, and how we can extend it to complex spaces.
History
Advisor
Gillet, Henri AChair
Gillet, Henri ADepartment
Mathematics, Statistics, and Computer SciencesDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral
Degree name
PhD, Doctor of PhilosophyCommittee Member
Antieau, David B Hurder, Steven E Shipley, Brooke E Higson, NigelSubmitted date
August 2019Thesis type
application/pdfLanguage
- en
Issue date
2019-08-27Usage metrics
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