| 書(shū)目名稱 | Lectures on Seiberg-Witten Invariants | | 編輯 | John Douglas Moore | | 視頻video | http://file.papertrans.cn/584/583596/583596.mp4 | | 叢書(shū)名稱 | Lecture Notes in Mathematics | | 圖書(shū)封面 |  | | 描述 | Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa- tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang- Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson‘s theory of "anti-self-dual" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE‘s. It is therefore quite surprising that there is a set of PDE‘s which are ev | | 出版日期 | Book 2001Latest edition | | 關(guān)鍵詞 | Characteristic class; Clifford algebras; Dirac operators; Hodge theory; Seiberg-Witten invariants; algebr | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-540-40952-6 | | isbn_softcover | 978-3-540-41221-2 | | isbn_ebook | 978-3-540-40952-6Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 2001 |
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