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Author: Peter Kronheimer Publisher: Cambridge University Press ISBN: 9780521184762 Category : Mathematics Languages : en Pages : 808
Book Description
Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg-Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides the first full discussion of a central part of the study of the topology of manifolds since the mid 1990s.
Author: Peter Kronheimer Publisher: Cambridge University Press ISBN: 9780521184762 Category : Mathematics Languages : en Pages : 808
Book Description
Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg-Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides the first full discussion of a central part of the study of the topology of manifolds since the mid 1990s.
Author: Francesco Lin Publisher: American Mathematical Soc. ISBN: 1470429632 Category : Floer homology Languages : en Pages : 162
Book Description
In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.
Author: Helmut Hofer Publisher: Birkhäuser ISBN: 3034892179 Category : Mathematics Languages : en Pages : 688
Book Description
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.
Author: Chris Wendl Publisher: Cambridge University Press ISBN: 1108759580 Category : Mathematics Languages : en Pages : 198
Book Description
Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef–White theorem.
Author: Liviu I. Nicolaescu Publisher: American Mathematical Soc. ISBN: 0821821458 Category : Four-manifolds (Topology) Languages : en Pages : 504
Book Description
After background on elliptic equations, Clifford algebras, Dirac operators, and Fredholm theory, chapters introduce solutions of the Seiberg-Witten equations and the group of gauge transformations, then look at algebraic surfaces. A final chapter presents in great detail a cut-and-paste technique for computing Seiberg-Witten invariants, covering elliptic equations on manifolds with cylindrical ends, finite energy monopoles on cylindrical manifolds, local and global properties of the moduli spaces of finite energy monopoles, and the process of reconstructing the space of monopoles on a 4-manifold decomposed into several parts by a hypersurface. Annotation copyrighted by Book News, Inc., Portland, OR.
Author: Nikolai Saveliev Publisher: Walter de Gruyter ISBN: 3110250365 Category : Mathematics Languages : en Pages : 220
Book Description
Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The proof of the three-dimensional Poincaré conjecture has rendered this application moot but hardly made Casson's contribution less relevant: in fact, a lot of modern day topology, including a multitude of Floer homology theories, can be traced back to his λ-invariant. The principal goal of this book, now in its second revised edition, remains providing an introduction to the low-dimensional topology and Casson's theory; it also reaches out, when appropriate, to more recent research topics. The book covers some classical material, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It then proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and concludes with a brief overview of recent developments. The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincaré duality on manifolds.
Author: Toshiki Mabuchi Publisher: CRC Press ISBN: 1000153444 Category : Mathematics Languages : en Pages : 244
Book Description
This volume contains papers presented at the 27th Taniguchi International Symposium, held in Sanda, Japan - focusing on the study of moduli spaces of various geometric objects such as Einstein metrics, conformal structures, and Yang-Mills connections from algebraic and analytic points of view.;Written by over 15 authorities from around the world, Einstein Metrics and Yang-Mills Connections...: discusses current topics in Kaehler geometry, including Kaehler-Einstein metrics, Hermitian-Einstein connections and a new Kaehler version of Kawamata-Viehweg's vanishing theorem; explores algebraic geometric treatments of holomorphic vector bundles on curves and surfaces; addresses nonlinear problems related to Mong-Ampere and Yamabe-type equations as well as nonlinear equations in mathematical physics; and covers interdisciplinary topics such as twistor theory, magnetic monopoles, KP-equations, Einstein and Gibbons-Hawking metrics, and supercommutative algebras of superdifferential operators.;Providing a wide array of original research articles not published elsewhere Einstein Metrics and Yang-Mills Connections is for research mathematicians, including topologists and differential and algebraic geometers, theoretical physicists, and graudate-level students in these disciplines.
Author: Peter Kronheimer
Author: Peter Kronheimer
Author: P. B. Kronheimer
Author: Kronheimer P B Mrowka Tomasz
Author: Peter Kronheimer
Author: Francesco Lin
Author: Helmut Hofer
Author: Chris Wendl
Author: Liviu I. Nicolaescu
Author: Nikolai Saveliev
Author: Toshiki Mabuchi