Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory

Released on by Abhijit Champanerkar
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  • Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory Book Detail

  • Author : Abhijit Champanerkar
  • Release Date : 2011
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 273
  • ISBN 13 : 0821849603
  • File Size : 2,2 MB
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Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory by Abhijit Champanerkar PDF Summary

Book Description: 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.

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Hyperbolic Knot Theory

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File Size : 39,39 MB
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This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was