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Topology and Geometry of Manifolds
Edited by: Gordana Matić and Clint McCrory, University of Georgia, Athens, GA
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Proceedings of Symposia in Pure Mathematics
2003; 357 pp; hardcover
Volume: 71
ISBN-10: 0-8218-3507-6
ISBN-13: 978-0-8218-3507-4
List Price: US$87
Member Price: US$69.60
Order Code: PSPUM/71
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Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots.

Articles of particular interest include John Etnyre's "Introductory Lectures on Contact Geometry", which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's "Problems in Low-Dimensional Contact Topology" and Danny Calegari's extensive paper,"Problems in Foliations and Laminations of 3-Manifolds", are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.

Readership

Graduate students and research mathematicians interested in the geometry and topology of manifolds.

Table of Contents

  • J. Roberts -- Rozansky-Witten theory
  • C. Connell and B. Farb -- Some recent applications of the barycenter method in geometry
  • S. Bigelow -- The Lawrence-Krammer representation
  • W. H. Meeks III -- Topological properties of properly embedded minimal surfaces in \(\mathbb{R}^3\)
  • J. B. Etnyre -- Introductory lectures on contact geometry
  • V. Colin, E. Giroux, and K. Honda -- On the coarse classification of tight contact structures
  • P. Ghiggini and S. Schönenberger -- On the classification of tight contact structures
  • M. Symington -- Four dimensions from two in symplectic topology
  • H. U. Boden, C. M. Herald, and P. Kirk -- On the integer valued SU(3) Casson invariant
  • P. M. N. Feehan and T. G. Leness -- On Donaldson and Seiberg-Witten invariants
  • J. S. Carter and M. Saito -- Quandle homology theory and cocycle knot invariants
  • T. Li -- Boundary train tracks of laminar branched surfaces
  • S. Schleimer -- Strongly irreducible surface automorphisms
  • D. Calegari -- Problems in foliations and laminations of 3-manifolds
  • J. B. Etnyre and L. L. Ng -- Problems in low dimensional contact topology
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