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E-raamat: Topology and Geometry of Manifolds

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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 in this title 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.
Preface vii
Rozansky-Witten theory
1(18)
Justin Roberts
Some recent applications of the barycenter method in geometry
19(32)
Christopher Connell
Benson Farb
The Lawrence-Krammer representation
51(18)
Stephen Bigelow
Topological properties of properly embedded minimal surfaces in R3
69(12)
William H. Meeks III
Introductory lectures on contact geometry
81(28)
John B. Etnyre
On the coarse classification of tight contact structures
109(12)
Vincent Colin
Emmanuel Giroux
Ko Honda
On the classification of tight contact structures
121(32)
Paolo Ghiggini
Stephan Schonenberger
Four dimensions from two in symplectic topology
153(56)
Margaret Symington
On the integer valued SU(3) Casson invariant
209(28)
Hans U. Boden
Christopher M. Herald
Paul Kirk
On Donaldson and Seiberg-Witten invariants
237(12)
Paul M. N. Feehan
Thomas G. Leness
Quandle homology theory and cocycle knot invariants
249(20)
J. Scott Carter
Masahico Saito
Boundary train tracks of laminar branched surfaces
269(18)
Tao Li
Strongly irreducible surface automorphisms
287(10)
Saul Schleimer
Problems in foliations and laminations of 3-manifolds
297(40)
Danny Calegari
Problems in low dimensional contact topology
337
John B. Etnyre
Lenhard L. Ng