Geometry and Physics -

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Résumé :
This important reference - based on the proceedings of the Special Session on Geometry and Physics held over a six-month period at the University of Aarhus, Denmark, and on articles from the summer school held at Odense University, Denmark - offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts, Geometry and Physics presents the Seiberg-Witten invariants that facilitate the solution of open problems in Donaldson's theory...describes applications of the Seiberg-Witten invariants...analyzes moduli spaces of semi-stable bundles over Riemann surfaces...addresses operator algebras and topology...demonstrates the planar topological aspects of subfactors...examines symplectic geometry and Einstein metrics...discusses novel ways of computing curvature and holonomy for the determinant line bundle...elucidates the new topic of finite type invariants of three-manifolds and relations with nonperturbative quantum invariants...delineates recent work on a purely topological approach to physics-inspired invariants...and much more. Generously illustrated and containing over 800 key bibliographic citations, Geometry and Physics is an indispensable resource for geometers, topologists, mathematical and theoretical physicists, and graduate-level students in these disciplines.

Sommaire:
Opening address: geometry and physics - where we going? Summer School notes: Floer homology, A-infinity categories and topological field theory; quantum field theory, equivalent cohomology, symplectic geometry, and moduli spaces of vector bundles on Riemann surfaces; notes on Seiberg-Witten invariants; an introduction to the topology of the moduli space of stable bundles on a Riemann surface; the fundamental theorem of Vassiliev invariants. Conference and workshop papers: configuration spaces and imbedding problems; topology of the space of SU(2)-monopoles in R3; recent progress on Kahler-Einstein metrics; the ODE system arising from cohomogeneity One Einstein metrics; Einstein metrics on complex surfaces; BPS states as symplectic invariants from string theory; determinants line bundles revisited; on representations of spin mapping class groups arising in spin TQFT; the symplectic S-Cobodism conjecture - a summary; Hamiltonian Torus action; a new proof of the convexity theorem for the poisson-lie moment map; symplectic 4-manifolds with b2+=1; compact manifolds with exceptional holonomy; fusion product of positive level representations and lie algebra homology; affine connections on involutive G-structures; observations on the topology of symmetric spaces; hyperkahler metrics on cotangent bundles of Hermitian symmetric spaces; decomposable self-dual manifolds; the SU infinity - Toda filed equation and special four-dimensional metrics; the structure of quaternionic Kahler quotients; overview and warmup example for perturbation theory with instantons; a note on free composition of subfactors. (Part contents).