The Floer Memorial Volume

ISBN-13: 9783034899482 / Angielski / Miękka / 2011 / 691 str.

Helmut Hofer; Clifford H. Taubes; Alan Weinstein

Opis

Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder

Spis treści

Floer’s work on monopoles.- Monopoles on asymptotically flat manifolds.- The configuration space of Yang-Mills-Higgs theory on asymptotically flat manifolds.- Instanton homology and Dehn surgery.- Some remarks on symplectic monodromy of Milnor fibrations.- Floer homology.- Topologie des systèmes de Moser en dimension quatre.- Morse-Bott theory and equivariant cohomology.- Some simple continuity properties of symplectic capacities.- Floer’s work on instanton homology, knots and surgery.- Fukaya-Floer homology and gluing formulae for polynomial invariants.- On generating families.- Floer’s infinite dimensional Morse theory and homotopy theory.- Periodic solutions of elliptic type for strongly nonlinear Hamiltonian systems.- Topology of 2-knots in ?4 and symplectic geometry.- The ends of the monopole moduli space over ?3#, (homology sphere): Part I.- The ends of the monopole moduli space over ?3#, (homology sphere): Part II.- Using Floer’s exact triangle to compute Donaldson invariants.- A symplectic fixed point theorem for toric manifolds.- Floer homology and Novikov rings.- Symplectic invariants and Hamiltonian dynamics.- An irrational ruled 4-manifold.- Floer cohomology of Lagrangian intersections and pseudoholomorphic discs, III: Arnold-Givental conjecture.- An obstacle to non-Lagrangian intersections.- A Mayer-Vietoris model for Donaldson-Floer theory.- The cup-product on the Thom-Smale-Witten complex, and Floer cohomology.- The symplectic structure on moduli space.- Chern-Simons gauge theory as a string theory.