UID:
edocfu_9959239113202883
Format:
1 online resource (xiii, 242 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88463-8
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1-107-36659-3
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1-107-37128-7
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1-107-36168-0
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1-107-36814-6
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1-299-40435-9
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1-107-36413-2
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0-511-62934-6
Series Statement:
London Mathematical Society lecture note series ; 151
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Title; Copyright; Contents; Contents of Volume 1; Contributors; Names of Participants; Introduction; Acknowledgements; PART 1: SYMPLECnC GEOMETRY; Introduction; Rational and ruled symplectic 4-manifolds; 1. INTRODUCTION; 2. STATEMENT OF RESULTS; 2.1 Theorem; 2.2 Theorem; 2.3 Note; 2.4 Theorem; 2.5 Lemma; 2.6 Theorem; 2.7 Corollary; 2.8 Corollary; 2.9 Proposition; 2.10 Note; 2.11 Theorem; References; Symplectic capacities; 1 Introduction; Acknowledgement; 2 Axioms and Consequences; 3 Some Special Symplectic Capacities; Displacement Energy
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Periodic Hamiltonian Trajectories and Capacities4 A capacity on Symp2n and the Weinstein conjecture; 5 Capacities and Instanton Homology; References; The nonlinear Maslov index; Legendre-Grassmann manifolds.; Discriminants.; The Morse Inequality.; The Calabi-Weinstein Invariant.; Generating functions.; The asymptotical Maslov index.; REFERENCES; Filling by holomorphic discs and its applications; 1. COMPLEX AND SYMPLECTIC RECOLLECTIONS; 1.1 J-Convexity; 1.2 Contact Structure on a ./-Convex Hypersurface; 1.3 Invariants of Legendrian Curves
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1.4 Complex Points of a Real Surface in an Almost Complex 4-Manifold1.5 Tame Almost Complex Manifolds; 2. FILLING BY HOLOMORPHIC DISCS; 3. COMPACTNESS AND REGULARITY PROPERTIES FOR FAMILIES OF HOLOMORPHIC DISCS; 3.1 φadmissible sets; 3.2 Partial and maximal fillings; 3.4 Existence of the maximal filling; 3.5 Graph of a filling; 3.6 Cutting A out of M; 4. SURFACES WHICH CAN BE FILLED BY HOLOMORPHIC DISCS; 5. MANIFOLDS BOUNDED BY A J-CONVEX SPHERE; 6. KILLING OF ELLIPTIC COMPLEX POINTS; 7. LEGENDRIAN KNOTS; 8. Prime decomposition of manifolds with a pseudo-convex boundary
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9. EXAMPLE OF A FAILURE OF THE FILLING PROPERTY10. OPEN QUESTIONS AND CONJECTURES; 10.1; 10.1.A; 10.2; 10.3; 10.4; 10.5; 10.6; 10.7; REFERENCES; PART 2: JONES/WITTEN THEORY; Introduction; New results in Chern-Simons theory; 1. GEOMETRIC QUANTIZATION; (a) The prototype case: affine space; (b): The torus; (c): The symplectic quotient; (d): The moduli space of representations; 2. THE GAUGE THEORY CASE; 3. LINK INVARIANTS; (a): Canonical quantization; (b): The Feynman integral approach; (c): Putting these approaches together; References; Geometric quantization of spaces of connections; REFERENCES
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Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for 5/(2, C)REFERENCES; Representations of braid groups; REFERENCES; PART 3: THREE-DIMENSIONAL MANIFOLDS; Introduction; An introduction to polyhedral metrics of non-positive curvature on 3-manifolds; 0 INTRODUCTION; 1 POLYHEDRAL METRICS OF NON-POSITIVE CURVATURE; I. Cubings with non-positive curvature.; II. Generalized cubings with non-positive curvature.; 2 CONSTRUCTING 3-MANIFOLDS WITH NICE METRICS; 3 SINGULAR INCOMPRESSIBLE SURFACES; 4 STRUCTURE OF THE SPHERE AT INFINITY
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5 COMPLETE POLYHEDRAL METRICS OF FINITE VOLUME AND DEHN SURGERY ON CUSPS
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English
Additional Edition:
ISBN 0-521-40001-5
Language:
English
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