Moduli Spaces Of Real Projective Structures On Surfaces

This comprehensive book introduces readers to the theory of real projective structures on surfaces, highlighting key concepts and applications.

The book Moduli Spaces Of Real Projective Structures On Surfaces serves as an excellent introduction to the emerging field of real projective manifolds. It provides a thorough overview of the theory surrounding real projective structures on surfaces and their associated moduli spaces. A key focus of the text is the appealing parameterization of moduli space, as discovered by Fock and Goncharov, which facilitates explicit descriptions and analyses of several essential characteristics. These characteristics encompass a natural Poisson structure, the implications of projective duality, holonomy representations, and the geometry of ends, among others.

Targeting two distinct audiences, Moduli Spaces Of Real Projective Structures On Surfaces is designed for both newcomers seeking foundational knowledge about real projective surfaces or manifolds, as well as those with some familiarity who wish to delve deeper into the geometric principles behind Fock and Goncharov's parameterization. The content is structured to be accessible to any mathematician interested in these topics, ensuring a self-contained presentation that requires minimal prerequisites.

Moreover, the book showcases various applications of Fock and Goncharov's parameterization of moduli space, including novel proofs of significant results by renowned mathematicians such as Teichmüller, Goldman, and Marquis. Published by the Mathematical Society of Japan and distributed by World Scientific Publishing Co., this work is aimed at a global audience eager to explore the intricate world of real projective structures.