## Floer Memorial VolumeAndreas 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 This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer.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 |

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### Contents

and Braam | 1 |

Floer | 43 |

Instanton homology and Dehn surgery | 77 |

I | 99 |

Atiyah M | 105 |

Austin DM and Braam | 123 |

Bates S M | 185 |

Braam PJ and Donaldson S | 195 |

Fintushel R and Stern | 435 |

Givental A | 445 |

Hofer H and Salomon | 483 |

Hofer H and Zehnder | 525 |

McDuff D | 539 |

An irrational ruled 4manifold | 545 |

Oh Y | 555 |

Polterovich L | 575 |

### Common terms and phrases

4-manifold algebra assume asymptotically boundary chain map Chern Chern-Simons closed string cobordism compact complex structure component compute consider const constant construction converges corresponding critical points defined Definition deformed denote diffeomorphism differential dimension disc Donaldson invariants embedding equation equivalence equivariant cohomology estimate exists fiber fibration field theory finite dimensional fixed points flat connections Floer homology gauge transformation geometry gluing gradient flow gradient lines Hamiltonian Hence Hofer holomorphic holomorphic spheres holonomy homology 3-sphere homotopy hypersurface implies induced instanton integral intersection isomorphism isotopy knot Lagrangian linear loop Math metric moduli space monopoles Moreover Morse function Morse theory Morse-Bott non-trivial nondegenerate open string operator orbits oriented pair periodic solutions perturbation proof of Theorem prove quotient restriction satisfies smooth spectral sequence submanifold subset subspace surgery symplectic manifold symplectic structure symplectomorphisms tangent topological torus trajectories transversal trivial unstable manifolds vanishes vector bundle vector field zero