| Title |
Handbook of Teichmüller Theory, Volume III ([EBook] /) / Athanase Papadopoulos |
| Added Personal Name |
Papadopoulos, Athanase |
| Publication |
Zuerich, Switzerland : : European Mathematical Society Publishing House, , 2012 |
| Physical Details |
1 online resource (874 pages) |
| Series |
IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 2523-5133 ; ; 17 |
| ISBN |
9783037196038 |
| Summary Note |
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.: |
| Contents note |
Introduction to Teichmüller theory, old and new, III /: Quasiconformal and BMO-quasiconformal homeomorphisms /: Earthquakes on the hyperbolic plane /: Kerckhoff’s lines of minima in Teichmüller space /: A tale of two groups: arithmetic groups and mapping class groups /: Simplicial actions of mapping class groups /: On the coarse geometry of the complex of domains /: Minimal generating sets for the mapping class group /: From mapping class groups to monoids of homology cobordisms: a survey /: A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces /: Asymptotically rigid mapping class groups and Thompson groups /: An introduction to moduli spaces of curves and their intersection theory /: Homology of the open moduli space of curves /: On the $L p$-cohomology and the geometry of metrics on moduli spaces of curves /: The Weil–Petersson metric and the renormalized volume of hyperbolic 3-manifolds /: Discrete Liouville equation and Teichmüller theory /: |
| Mode of acces to digital resource |
Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.4171/103 |
| See Also |
https://www.ems-ph.org/img/books/irma17_mini.jpg |
| Links to Related Works |
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