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Full Description
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston's heritage. Thurston's ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston's norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
Contents
1 Ken'ichi Ohshika and Athanase Papadopoulos, Introduction.- 2 Michael Kapovich, A survey of complex hyperbolic Kleinian groups.- 3 Graham Smith, Möbius structures, hyperbolic ends and K-surfaces in hyperbolic space.- 4 Joan Porti, Cone 3-manifods.- 5 Takahiro Kitayama, A survey of the Thurston norm.- 6 Georgios Kydonakis, From hyperbolic Dehn filling to surgeries in representation varieties.- 7 Sang-Hyun Kim, Acute geodesic triangulations of manifolds.- 8 Ismail Sağlam, Signature calculation of the area Hermitian form on some spaces of polygons.- 9 Mikhail Chernaviskikh, Altan Erdnigor, Nikita Kalinin, and Alexandr Zakharov, Equilateral convex triangulations of RP2 with three conical points of equal defect.- 10 Mahan Mj and Sabyasachi Mukherjee, Combination theorems in groups, geometry and dynamics.- 11 Kevin Pilgrim, On the pullback relation on curves induced by a Thurston map.- 12 William Floyd, The pullback map on Teichmüller space induced from a Thurston map.- 13 Russell Lodge, Yauhen Mikulich and Dierk Schleicher, A classification of postcritically finite Newton maps.- 14 Sarah Rees, The development of the theory of automatic groups.- 15 Thomas Koberda, Geometry and combinatorics via right-angled Artin groups.
