This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students. Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories: (1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants; (2) the geometry associated to triangulations of hyperbolic 3-manifolds; (3) arithmetic invariants of hyperbolic 3-manifolds; (4) quantum invariants associated to knots and hyperbolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.This turns out to imply Weila#39;s local rigidity theorem, as we shall show in Theorem 6.4. 1.3. A readera#39;s guide. For a relative novice ... Skim over Section 2, as needed , to recall the crucial defini- tions of gluing equations and holonomy. ... The metric models for the tetrahedra in M come from ideal tetrahedra in H3: Definition 2.1.
|Title||:||Interactions Between Hyperbolic Geometry, Quantum Topology, and Number Theory|
|Publisher||:||American Mathematical Soc. - 2011|