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# 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 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

2019-08-27## Usage metrics

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## Licence

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