Intersection theory on moduli spaces of curves ... - User Web Pages

iiiPrefaceChapter 1 is a review of known results concerning moduli spaces of curves, with the appropriatereferences to the literature contained therein.Chapter 2 includes results obtained in collaboration with Paul Norbury. More specifically, Section2.1, Section 2.2 and parts of Section 2.4 contain the basic content of the joint paper [9],though substantially rewritten and elaborated on, from my own perspective. Section 2.3 andthe remaining parts of Section 2.4 constitute wholly original work.Chapter 3 is the product of my own research, although some of the ideas have been drawnfrom various sources in the literature. In particular, the proof of Theorem 3.9 parallels the workof Bowditch and Epstein [5]. Furthermore, the concluding arguments in this chapter followthe structure of Kontsevich’s proof of his combinatorial formula [26]. We note that Section 3.4essentially reproduces the results appearing in Appendix C of Kontsevich’s paper, though theexposition is greatly expanded to include more thorough and more elementary proofs.