Gauge theory and the topology of four-manifolds
著者
書誌事項
Gauge theory and the topology of four-manifolds
(IAS/Park City mathematics series / [Dan Freed, series editor], v. 4)
American Mathematical Society, c1998
大学図書館所蔵 全53件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
"Lecture notes from the Graduate Summer School program on gauge theory and smooth 4-manifolds held in Park City, Utah, on July 10-30, 1994." -- T.p. verso
Includes bibliographical references
内容説明・目次
内容説明
The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying $SU(2)$-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space.One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kahler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the $SU(2)$ - moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. It is for this reason that the results presented in this volume will be essential.
目次
Geometric invariant theory and the moduli of bundles: Geometric invariant theory by D. Gieseker The numerical criterion by D. Gieseker The moduli of stable bundles by D. Gieseker References by D. Gieseker Anti-self-dual connections and stable vector bundles: Hermitian bundles, Hermitian connections and their curvatures by J. Li Hermitian-Einstein connections and stable vector bundles by J. Li The existence of Hermitian-Einstein metrics by J. Li References by J. Li An introduction to gauge theory: The context of Gauge theory by J. W. Morgan Principal bundles and connections by J. W. Morgan Curvature and characteristic classes by J. W. Morgan The space of connections by J. W. Morgan The ASD equations and the moduli space by J. W. Morgan Compactness and gluing theorems by J. W. Morgan The Donaldson polynomial invariants by J. W. Morgan The connected sum theorem by J. W. Morgan References by J. W. Morgan Computing Donaldson invariants: Overview by R. J. Stern -2 spheres and the blowup formula by R. J. Stern Simple-type criteria and elliptic surfaces by R. J. Stern Elementary rational blowdowns by R. J. Stern Taut configurations and Horikowa surfaces by R. J. Stern References by R. J. Stern Donaldson-Floer theory: Introduction by C. Taubes and J. A. Bryan Quantization by C. Taubes and J. A. Bryan Simplicial decomposition of $\Cal{M}^0_X$ by C. Taubes and J. A. Bryan Half-infinite dimensional spaces by C. Taubes and J. A. Bryan References by C. Taubes and J. A. Bryan.
「Nielsen BookData」 より