SARTIPI-DISSERTATION-2019.pdf (635.41 kB)

Paschke Category, K-homology, and the Riemann-Roch Transformation

Download (635.41 kB)
thesis
posted on 01.08.2019, 00:00 by Khashayar Sartipi
For 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 A

Chair

Gillet, Henri A

Department

Mathematics, Statistics, and Computer Sciences

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Degree name

PhD, Doctor of Philosophy

Committee Member

Antieau, David B Hurder, Steven E Shipley, Brooke E Higson, Nigel

Submitted date

August 2019

Thesis type

application/pdf

Language

en

Issue date

27/08/2019

Exports

Categories

Exports