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1. Table of Contents for the Introduction and Chapters from Riemann's Existence Theorem: An elementary approach to moduli. Commissioned by Cambridge University Press. To Table of Contents! tableofcontents.pdf

2. Chapter 1: Scope of the Existence Theorem: An over view of the whole book: Joining Modular Towers and the Grothendieck-Teichmuller group for their ability to create useful moduli spaces. Includes the relation between classical theta functions, Eisenstein series and the Inverse Galois problem. Last revision: 10/10/02: prelude.html %-%-% prelude.pdf

3. Chap. 2: Analytic Continuation: The first text chapter, on Analytic continuation and an introduction to algebraic functions. Rooted solidly in quotations from Ahlfors. Latest Revision: 02/05/03. chpanal.html %-%-% chpanal.pdf

4. Chap. 3: Complex Manifolds and Covers: Introduces coordinates on a Riemann surface, and sufficient algebraic geometry to consider manifold compactifications of common Riemann surfaces. Aims directly at introducing Riemann's favorite subject -- necessary for his solution to the Jacobi Inversion Problem -- half-canonical classes. The detail on covering spaces, Galois covers and flat bundles goes beyond what is usual for a truly graduate level book. Latest Revision: 02/05/03. chpfund.pdf

5. Chap. 4: Riemann's Existence Theorem: I temporarily divided this into two parts: chpret.pdf the first part is in pretty good shape, while the second part chpret2.pdf is still undergoing revision. The proof, combinatorics of its use (including Braid and Hurwitz monodromy group manipulations), and the algebra of coordinates attached to Riemann's Existence Theorem. We give a non-traditional approach to Abel's Theorem for genus 1 curves. This treatment of the j(\tau) and \lambda(\tau) functions and modular curves of complex variables motivates Chap. 5: Hurwitz monodromy and the development of Modular Towers. Updates (mostly) on Chap. 4 will continue through February while Work on Chap. 5 will continue during the semester I'm spending at University of Florida, to the end of March, 2003 and when I'm back in California until the middle of June. It should be ready for the publisher by then. Latest Revision: 02/26/03. chpret4-firsthalf.pdf

6. A three page bibliography. bib.pdf

7. The slides for the talk: What Gauss told Riemann about Abel's Theorem! Talk given at the Florida Mathematics History lecture, during a semester in Honor of John Thompson's 70th birthday in 2003. flortalk.pdf

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