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Geometry of Low-Dimensional Manifolds: Volume 2 : Symplectic Manifolds and Jones-Witten Theory - S. K. Donaldson

Geometry of Low-Dimensional Manifolds: Volume 2

Symplectic Manifolds and Jones-Witten Theory

By: S. K. Donaldson (Editor), C. B. Thomas (Editor)

Paperback

Published: 25th March 1991
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These volumes are 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 (topology, differential and algebraic geometry and mathematical physics) interact.

Contents of Volume 1p. vi
Contributorsp. vii
Names of Participantsp. viii
Introductionp. xi
Acknowledgementsp. xiv
Symplectic Geometryp. 1
Introductionp. 3
Rational and ruled symplectic 4-manifoldsp. 7
Symplectic capacitiesp. 15
The nonlinear Maslov indexp. 35
Filling by holomorphic discs and its applicationsp. 45
Jones/Witten Theoryp. 69
Introductionp. 71
New results in Chern-Simons theoryp. 73
Geometric quantization of spaces of connectionsp. 97
Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for s/(2, C)p. 101
Representations of braid groupsp. 115
Three-Dimensional Manifoldsp. 123
Introductionp. 125
An introduction to polyhedral metrics of non-positive curvature on 3-manifoldsp. 127
Finite groups of hyperbolic isometriesp. 163
Pin structures on low-dimensional manifoldsp. 177
Contents of Volume 2p. vi
Contributorsp. vii
Names of Participantsp. viii
Introductionp. ix
Acknowledgmentsp. xiv
Four-Manifolds and Algebraic Surfacesp. 1
Yang-Mills invariants of four-manifoldsp. 5
On the topology of algebraic surfacesp. 41
The topology of algebraic surfaces with q = pg = 0p. 55
On the Homeomorphism classification of smooth knotted surfaces in the 4-spherep. 63
Flat algebraic manifoldsp. 73
Floer's Instanton Homology Groupsp. 93
Instanton homology, surgery and knotsp. 97
Instanton homologyp. 115
Invariants for homology 3-spheresp. 125
On the Floer homology of Seifert fibered homology 3-spheresp. 149
Z[subscript a]-invariant SU(2) instantons over the four-spherep. 161
Differential Geometry and Mathematical Physicsp. 175
Skyrme fields and instantonsp. 179
Representations of braid groups and operators coupled to monopolesp. 191
Extremal immersions and the extended frame bundlep. 207
Minimal surfaces in quaternionic symmetric spacesp. 231
Three-dimensional Einstein-Weyl geometryp. 237
Harmonic Morphisms, conformal foliations and Seifert fibre spacesp. 247
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521400015
ISBN-10: 0521400015
Series: London Mathematical Society Lecture Note Series : Book 2
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 260
Published: 25th March 1991
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.5
Weight (kg): 0.39