A Introduction to the Mapping Class Group and Symplectic Floer Homology
A Introduction to the Mapping Class Group and Symplectic Floer Homology

Author: Michael Jia Ming Lin

Publisher:

Published: 2019

Total Pages: 0

ISBN-13:

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We give an introduction to the mapping class group and the Nielsen-Thurston classification, as well as the construction of symplectic Floer homology. Some analytical details are provided, in hopes of familiarizing the reader with the language of the proofs common in the many varieties of Floer homology. Recent developments in symplectic Floer homology are summarized in the case of surfaces, based on the mapping class of the symplectomorphism. Those who would like a first pass of the technical details of Floer theory and see an application beyond the Arnold conjecture would be suitable readers.

The Topology of 4-Manifolds
The Topology of 4-Manifolds

Author: Robion C. Kirby

Publisher: Springer

Published: 2006-11-14

Total Pages: 114

ISBN-13: 354046171X

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This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

The Floer Memorial Volume
The Floer Memorial Volume

Author: Helmut Hofer

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 688

ISBN-13: 3034892179

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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.