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Different faces of geometry

著者: S K Donaldson; Y Eliashberg; Mikhael Gromov
出版商: New York : Kluwer Academic/Plenum Publishers, ©2004.
丛书: International mathematical series.
版本/格式:   电子图书 : 文献 : 英语查看所有的版本和格式
数据库:WorldCat
提要:
Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: Amoebas and Tropical Geometry Convex Geometry and Asymptotic Geometric Analysis Differential Topology of 4-Manifolds 3-Dimensional Contact Geometry Floer Homology and  再读一些...
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类型/形式: Electronic books
附加的形体格式: Print version:
Different faces of geometry.
New York : Kluwer Academic/Plenum Publishers, ©2004
(DLC) 2004051669
(OCoLC)55518031
材料类型: 文献, 互联网资源
文件类型: 互联网资源, 计算机文档
所有的著者/提供者: S K Donaldson; Y Eliashberg; Mikhael Gromov
ISBN: 030648658X 9780306486586
OCLC号码: 57056142
描述: 1 online resource (xxi, 404 pages) : illustrations.
内容: Refined Seiberg --
Witten Invariants --
3-Dimensional Methods in Contact Geometry. --
Asymptotic Convex Geometry --
Short Overview. --
Singularities of Special Lagrangian Submanifolds --
Curvature Functionals, Optimal Metrics, and the Differential Topology of 4-Manifolds --
Amoebas of Algebraic Varieties and Tropical Geometry --
Heegaard Diagrams and Holomorphic Disks --
Exact Lagrangian Submanifolds in T*Sn and the Graded Kronecker Quiver.
丛书名: International mathematical series.
责任: edited by Simon Donaldson, Yakov Eliashberg and Mikhael Gromov.

摘要:

Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: Amoebas and Tropical Geometry Convex Geometry and Asymptotic Geometric Analysis Differential Topology of 4-Manifolds 3-Dimensional Contact Geometry Floer Homology and Low-Dimensional Topology Khler Geometry Lagrangian and Special Lagrangian Submanifolds Refined Seiberg-Witten Invariants. These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvth (USA) and Z. Szab (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). "One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in low-dimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvth and Szab). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun. Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Khler and algebraic manifolds), a point which is also made by Bauer in the context of 4-manifolds and the "11/8 conjecture". LeBrun's article gives another perspective on 4-manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even "well-known" 4-manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the "geometry" is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra. The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebro-topological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems."--The Preface by the Editors.

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