Ebook: The Floer Memorial Volume

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 This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer.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

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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 This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer.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
Content:
Front Matter....Pages i-xii
Floer’s work on monopoles....Pages 1-2
Monopoles on asymptotically flat manifolds....Pages 3-41
The configuration space of Yang-Mills-Higgs theory on asymptotically flat manifolds....Pages 43-75
Instanton homology and Dehn surgery....Pages 77-97
Some remarks on symplectic monodromy of Milnor fibrations....Pages 99-103
Floer homology....Pages 105-108
Topologie des syst?mes de Moser en dimension quatre....Pages 109-122
Morse-Bott theory and equivariant cohomology....Pages 123-183
Some simple continuity properties of symplectic capacities....Pages 185-193
Floer’s work on instanton homology, knots and surgery....Pages 195-256
Fukaya-Floer homology and gluing formulae for polynomial invariants....Pages 257-281
On generating families....Pages 283-296
Floer’s infinite dimensional Morse theory and homotopy theory....Pages 297-325
Periodic solutions of elliptic type for strongly nonlinear Hamiltonian systems....Pages 327-333
Topology of 2-knots in ?4 and symplectic geometry....Pages 335-353
The ends of the monopole moduli space over ?3# (homology sphere): Part I....Pages 355-408
The ends of the monopole moduli space over ?3# (homology sphere): Part II....Pages 409-434
Using Floer’s exact triangle to compute Donaldson invariants....Pages 435-444
A symplectic fixed point theorem for toric manifolds....Pages 445-481
Floer homology and Novikov rings....Pages 483-524
Symplectic invariants and Hamiltonian dynamics....Pages 525-544
An irrational ruled symplectic 4-manifold....Pages 545-554
Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks, III: Arnold-Givental Conjecture....Pages 555-573
An obstacle to non-Lagrangian intersections....Pages 575-586
A Mayer-Vietoris model for Donaldson-Floer theory....Pages 587-608
The cup-product on the Thom-Smale-Witten complex, and Floer cohomology....Pages 609-625
The symplectic structure on moduli space....Pages 627-635
Chern-Simons gauge theory as a string theory....Pages 637-678
Back Matter....Pages 679-691

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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
Content:
Front Matter....Pages i-xii
Floer’s work on monopoles....Pages 1-2
Monopoles on asymptotically flat manifolds....Pages 3-41
The configuration space of Yang-Mills-Higgs theory on asymptotically flat manifolds....Pages 43-75
Instanton homology and Dehn surgery....Pages 77-97
Some remarks on symplectic monodromy of Milnor fibrations....Pages 99-103
Floer homology....Pages 105-108
Topologie des syst?mes de Moser en dimension quatre....Pages 109-122
Morse-Bott theory and equivariant cohomology....Pages 123-183
Some simple continuity properties of symplectic capacities....Pages 185-193
Floer’s work on instanton homology, knots and surgery....Pages 195-256
Fukaya-Floer homology and gluing formulae for polynomial invariants....Pages 257-281
On generating families....Pages 283-296
Floer’s infinite dimensional Morse theory and homotopy theory....Pages 297-325
Periodic solutions of elliptic type for strongly nonlinear Hamiltonian systems....Pages 327-333
Topology of 2-knots in ?4 and symplectic geometry....Pages 335-353
The ends of the monopole moduli space over ?3# (homology sphere): Part I....Pages 355-408
The ends of the monopole moduli space over ?3# (homology sphere): Part II....Pages 409-434
Using Floer’s exact triangle to compute Donaldson invariants....Pages 435-444
A symplectic fixed point theorem for toric manifolds....Pages 445-481
Floer homology and Novikov rings....Pages 483-524
Symplectic invariants and Hamiltonian dynamics....Pages 525-544
An irrational ruled symplectic 4-manifold....Pages 545-554
Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks, III: Arnold-Givental Conjecture....Pages 555-573
An obstacle to non-Lagrangian intersections....Pages 575-586
A Mayer-Vietoris model for Donaldson-Floer theory....Pages 587-608
The cup-product on the Thom-Smale-Witten complex, and Floer cohomology....Pages 609-625
The symplectic structure on moduli space....Pages 627-635
Chern-Simons gauge theory as a string theory....Pages 637-678
Back Matter....Pages 679-691
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