Handbook of Teichmüller Theory, Volume III [electronic resource] / Athanase Papadopoulos

Introduction to Teichmüller theory, old and new, III / Athanase Papadopoulos -- Quasiconformal and BMO-quasiconformal homeomorphisms / Jean-Pierre Otal -- Earthquakes on the hyperbolic plane / Jun Hu -- Kerckhoff’s lines of minima in Teichmüller space / Caroline Series -- A tale of two groups: arithmetic groups and mapping class groups / Lizhen Ji -- Simplicial actions of mapping class groups / John D. McCarthy, Athanase Papadopoulos -- On the coarse geometry of the complex of domains / Valentina Disarlo -- Minimal generating sets for the mapping class group / Mustafa Korkmaz -- From mapping class groups to monoids of homology cobordisms: a survey / Kazuo Habiro, Gwénaël Massuyeau -- A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces -- Asymptotically rigid mapping class groups and Thompson groups / Louis Funar, Christophe Kapoudjian, Vlad Sergiescu -- An introduction to moduli spaces of curves and their intersection theory / Dimitri Zvonkine -- Homology of the open moduli space of curves / Ib Madsen -- On the $L^p$-cohomology and the geometry of metrics on moduli spaces of curves / Lizhen Ji, Steven Zucker -- The Weil–Petersson metric and the renormalized volume of hyperbolic 3-manifolds / Kirill Krasnov, Jean-Marc Schlenker -- Discrete Liouville equation and Teichmüller theory / Rinat Kashaev.

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The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with 3-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas towards a unique subject is a manifestation of the unity and harmony of mathematics. The present volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in the fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. The metric and the analytic theory. The group theory. The algebraic topology of mapping class groups and moduli spaces. Teichmüller theory and mathematical physics. The handbook is addressed to graduate students and researchers in all the fields mentioned.