Geometry and Physics

ISBN-13: 9781138430389 / Angielski / Twarda / 2017

H. Pedersen

Opis

Based on the proceedings of the Special Session on Geometry and Physics held at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark, this title offers various contributions on the topics that involve physics, geometry, and topology. It is written by more than 50 international experts.

Spis treści

Contents -- Preface -- Contributors -- Opening Address -- Geometry and physics: where are we going? /Sir Michael Atiyah -- Summer School Notes -- Floer homology, A?-categories and topological field theory /Kenji Fukaya, notes by Paul Seidel -- Quantum field theory, equivariant cohomology, symplectic geometry and moduli spaces of vector bundles on Riemann surfaces /Lisa C. Jeffrey -- Notes on Seiberg-Witten invariants /Zoltdn Szabo -- An introduction to the topology of the moduli space of stable bundles on a Riemann surface /Michael Thaddeus -- The fundamental theorem of Vassiliev invariants /Dror Bar-Natan, notes by Alexander Stoimenow -- Conference and Workshop Papers -- Configuration spaces and imbedding problems /Raoul Bott -- Topology of the space of SU(2)-monopoles in M3 /Graeme Segal -- Recent progress on Kahler-Einstein metrics /Gang Tian -- The ODE system arising from cohomogeneity one Einstein metrics /J.-H. Eschenburg and McKenzie Y. Wang -- Einstein metrics on complex surfaces /Claude LeBrun -- BPS states as symplectic invariants from string theory /Shing-Tung Yau and Eric Zaslow -- Determinant line bundles revisited /Daniel S. Freed -- On representations of spin mapping class groups arising in Spin TQFT /G. Masbaum -- The symplectic S-cobordism conjecture: a summary /Kenji Fukaya -- Hamiltonian torus actions /Yael Karshon -- A new proof of the convexity theorem for the Poisson-Lie moment map /A. Yu. Alekseev -- Symplectic 4-manifolds with = 1 /Hiroshi Ohta and Kaoru Ono -- Compact manifolds with exceptional holonomy /Dominic Joyce -- Fusion product of positive level representations and Lie algebra homology /Shrawan Kumar -- Affine connections on involutive G'-structures /Sergey A. Merkulov -- Observations on the topology of symmetric spaces /A. Fino and S. Salamon -- Hyperkahler metrics on cotangent bundles of Hermitian symmetric spaces /Olivier Biquard and Paul Gauduchon -- Decomposable self-dual manifolds /Y. S. Boon -- The SJ7(oo)-Toda field equation and special four-dimensional metrics /K. P. Tod -- The structure of quaternionic Kahler quotients /Andrew Dancer and Andrew Swann -- Overview and warmup example for perturbation theory with instantons /Scott Axelrod -- A note on free composition of subfactors /Dietmar Bisch and Vaughan Jones -- Witten-Reshetikhin-Turaev invariants of 3-manifolds as holomorphic functions /R. J. Lawrence -- On finite type invariants of links and rational homology spheres derived from the Jones polynomial and Witten-Reshetikhin-Turaev invariant /L. Rozansky -- A quantum s /2-invariant of 3-manifolds which contains all the Witten-Reshetikhin-Turaev invariants /Thang T. Q. Le -- On some invariants of 3-manifolds /Tomotada Ohtsuki -- Quantum Sp(2) invariants of three-manifolds at eighth and tenth roots of unity /Hitoshi Murakami and Tomotada Ohtsuki -- On finite type 3-manifold invariants V: rational homology 3-spheres /Stavros Garoufalidis and Tomotada Ohtsuki -- The Casson invariant for a knot in a 3-manifold /Jun Murakami -- Invariants of links and three-manifolds via Hopf algebras /Louis H. Kauffman -- Portrait of the handle as a Hopf algebra /David Yetter -- Genealogy of non-perturbative quantum-invariants of 3-manifolds: the surgical family /Thomas Kerler -- Finite order invariants of framed knots in a solid torus and in Arnold’s J+-theory of plane curves /V. Goryunov -- Numerical application of quantum invariants to random knotting /Tetsuo Deguchi and Kyoichi Tsurusaki -- Non-Abelian monopoles and vortices /Steven B. Bradlow and Oscar Garcia-Prada -- Seiberg-Witten and Gromov invariants /Clifford H. Taubes -- Introduction to conformal field theory with gauge symmetries /Kenji Ueno.

O autorze

Denmark. Dr. Andersen received the D.Phil. degree (l992) in mathematics from the University of Oxford, England. Johan Dupont is Special Associate Professor of Mathematics at Aarhus University, Denmark. Dr. Dupont received the Ph.D. degree (l 972) in mathematics from Aarhus University, Denmark. Henrik Pedersen is a Lecturer in Mathematics at Odense University, Denmark. He received the D.Phil. degree (l 985) in mathematics from the University of Oxford, England. Andrew Swann is a Lecturer in Mathematics in the School of Mathematical Sciences at the University of Bath, England. His qualifications include the D.Phil. degree in mathematics from the University of Oxford, England.