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題 名 | Cauchy-Riemann Geometry and Contact Topology in Three Dimensions=三維柯西黎曼幾何與觸結構拓樸 |
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作 者 | 鄭日新; | 書刊名 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
卷 期 | 24:2 2000.03[民89.03] |
頁 次 | 頁87-94 |
分類號 | 315.22 |
關鍵詞 | 柯西黎曼; 幾何; 觸結構; 拓樸; Cauchy-riemann geometry; Contact structure; Contact torsion; Monopole equation; Smale conjecture; |
語 文 | 英文(English) |
英文摘要 | We introduce a global Cauchy-Riemann (CR)-invariant and discuss its behavior on the moduli space of CR-structures. We argue that this study is related to the Smale conjecture in 3-topology and the problem of counting complex structures. Furthermore, we propose a contact-analogue of Ray-Singer's analytic torsion. This "contact torsion" is expected to be able to distinguish among "contact lens" spaces. We also propose the study of a certain kind of monopole equation associated with a contact structure. |
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