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The geometry of moduli spaces of pointed curves, the tensor product in the theory of Frobenius manifolds and the explicit Künneth formula in quantum cohomology. (English) Zbl 0918.14011
Bonner Mathematische Schriften. 312. Bonn: Univ. Bonn, Mathematisch-Naturwissenschaftliche Fakultät, 95 p. (1998).
This thesis develops further the results of an article by R. Kaufmann, Yu. Manin and D. Zagier [Commun. Math. Phys. 181, No. 3, 763-787 (1996; Zbl 0890.14011)] and their applications.
It has three chapters. The first one discusses the intersection of strata classes in $$\overline M_{g,n}$$ and provides the formulae for the intersection matrices in cohomology of $$\overline{M_{0,n}}$$ (moduli space of pointed curves of genus 0), and for Weil-Petersson volumes. These results are used in chapter two to define the tensor product of the pointed Frobenius manifolds. In chapter 3 the formulae from chapters 1 and 2 are used to derive the explicit Künneth formula for quantum cohomology. Examples of products of two and three 3-dimensional Calabi-Yau manifolds are discussed at the end.

MSC:
 14H10 Families, moduli of curves (algebraic) 14F99 (Co)homology theory in algebraic geometry 55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory