| 书目名称 | Lectures on Seiberg-Witten Invariants | | 编辑 | John Douglas Moore | | 视频video | | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 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 | | 关键词 | 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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发表于 2025-3-21 17:07:01
