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Geometry of Low-Dimensional Manifolds

Symplectic Manifolds and Jones-Witten Theory

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Paperback | 25 March 1991

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260 Pages

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This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects interact (for example: topology, differential and algebraic geometry and mathematical physics). The workshop brought together a number of distinguished figures to give lecture courses and seminars in these subjects; the volume that has resulted is the only expository source for much of the material, and will be essential for all research workers in geometry and mathematical physics.

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Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Algebraic Geometry Applied Mathematics Topology

Contents of Volume 1	p. vi
Contributors	p. vii
Names of Participants	p. viii
Introduction	p. xi
Acknowledgements	p. xiv
Symplectic Geometry	p. 1
Introduction	p. 3
Rational and ruled symplectic 4-manifolds	p. 7
Symplectic capacities	p. 15
The nonlinear Maslov index	p. 35
Filling by holomorphic discs and its applications	p. 45
Jones/Witten Theory	p. 69
Introduction	p. 71
New results in Chern-Simons theory	p. 73
Geometric quantization of spaces of connections	p. 97
Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for s/(2, C)	p. 101
Representations of braid groups	p. 115
Three-Dimensional Manifolds	p. 123
Introduction	p. 125
An introduction to polyhedral metrics of non-positive curvature on 3-manifolds	p. 127
Finite groups of hyperbolic isometries	p. 163
Pin structures on low-dimensional manifolds	p. 177
Contents of Volume 2	p. vi
Contributors	p. vii
Names of Participants	p. viii
Introduction	p. ix
Acknowledgments	p. xiv
Four-Manifolds and Algebraic Surfaces	p. 1
Yang-Mills invariants of four-manifolds	p. 5
On the topology of algebraic surfaces	p. 41
The topology of algebraic surfaces with q = pg = 0	p. 55
On the Homeomorphism classification of smooth knotted surfaces in the 4-sphere	p. 63
Flat algebraic manifolds	p. 73
Floer's Instanton Homology Groups	p. 93
Instanton homology, surgery and knots	p. 97
Instanton homology	p. 115
Invariants for homology 3-spheres	p. 125
On the Floer homology of Seifert fibered homology 3-spheres	p. 149
Z[subscript a]-invariant SU(2) instantons over the four-sphere	p. 161
Differential Geometry and Mathematical Physics	p. 175
Skyrme fields and instantons	p. 179
Representations of braid groups and operators coupled to monopoles	p. 191
Extremal immersions and the extended frame bundle	p. 207
Minimal surfaces in quaternionic symmetric spaces	p. 231
Three-dimensional Einstein-Weyl geometry	p. 237
Harmonic Morphisms, conformal foliations and Seifert fibre spaces	p. 247
Table of Contents provided by Syndetics. All Rights Reserved.

Geometry of Low-Dimensional Manifolds

Symplectic Manifolds and Jones-Witten Theory

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Paperback

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