Moduli spaces of real projective structures on surfaces / Alex Casella, Dominic Tate, Stephan Tillmann.

Casella, Alex [Browse]
Tokyo : Mathematical Society of Japan, 2020.
1 online resource (122 pages).


Summary note
"This book is an excellent first encounter with the burgeoning field of real projective manifolds. It gives a comprehensive introduction to the theory of real projective structures on surfaces and their moduli spaces. A central theme is an attractive parameterisation of moduli space discovered by Fock and Goncharov that allows the explicit description or analysis of many key features. These include a natural Poisson structure, the effect of projective duality, holonomy representations and the geometry of ends, to name but a few. This book is written with two kinds of readers in mind: those who would like to learn about real projective surfaces or manifolds, and those who have a passing knowledge thereof but are interested in the geometric underpinnings of Fock and Goncharov's parameterisation of moduli space of certain real projective structures. The material is accessible to any mathematician interested in these topics. It is presented in a self-contained manner with minimal prerequisites. Applications of Fock and Goncharov's parameterisation of moduli space presented in this book include new proofs of results by Teichm|ller (1939) concerning hyperbolic structures, by Goldman (1990) concerning closed surfaces, and by Marquis (2010) concerning structures of finite area."--Publisher.
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Includes bibliographical references.
Source of description
Description based on publisher supplied metadata and other sources.
  • Overview
  • Projective structures on surfaces
  • Ratios and configurations of flags
  • The parametrisation of the moduli spaces
  • Properties of the parametrisation
  • Applications of the parametrisation.
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