姓名 |
廖欣瑩(Sin-Ying Liao)
查詢紙本館藏 |
畢業系所 |
數學系 |
論文名稱 |
(Riemann-Roch-Hirzebruch Theorem For Circle Bundle Over A Riemann Surface)
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相關論文 | |
檔案 |
[Endnote RIS 格式]
[Bibtex 格式]
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摘要(中) |
鄭老師、蕭老師和蔡老師最近有一個定理,是在有 circle action 的 CR manifolds 上的 CR Riemann-Roch-Hirzebruch 定理。我們先複習在 Riemann surfaces 上的 Riemann-Roch-Hirzebruch 定理,然後再討論鄭老師、蕭老師和蔡老師在 CR manifolds 上 circle bundle 的 CR Riemann-Roch-Hirzebruch 定理。 |
摘要(英) |
In a recent paper of Cheng, Hsiao and Tsai, they obtained a CR Riemann-Roch-Hirzebruch Theorem for CR manifolds with a circle action. In this thesis we first review the Riemann-Roch-Hirzebruch Theorem for Riemann surfaces. Then we discuss CR Riemann-Roch-Hirzebruch Theorem of Cheng, Hsiao and Tsai for a circle bundle over a Riemann surface in details. |
關鍵字(中) |
★ 黎曼面 |
關鍵字(英) |
★ Hirzebruch-Riemann-Roch |
論文目次 |
1 Introduction..............1
2 Riemann-Roch-Hirzebruch Theorem for a Riemann Surface.....................2
2.1 Riemann-Roch Theorem...2
2.2 Characteristic Classes....6
2.3 Riemann-Roch-Hirzebruch Theorem for a Riemann surface....8
3 Riemann-Roch-Hirzebruch Theorem for a circle bundle over a Riemann surface...............11
3.1 Set up and terminology...............11
3.2 Riemann-Roch-Hirzebruch theorem On Circle Bundles........................13
3.2.1 Tangential Character Classes for circle bundle over a Riemann Surface.........25
3.2.2 Main Theorem............28
4 參考文獻……………………………………………………………………………………………………30 |
參考文獻 |
[1] M.-S. Baouendi and L.-P. Rothschild and F.-Treves, extit{CR structures with group action and extendability of CR functions}, Invent. Math., 83(1985), 359-396.
[2] J.-H. Cheng, C.-Y. Hsiao, I.-H. Tsai, extit{Heat Kernel, Asymptotics And A Local Index Theorem For CR Manifolds With $S^1$ Action}, arXiv:1511.00063v2.
[3] X. Dai, extit{Lectures on Dirac Operators and Index Theory}, January 7, 2015.
[4] X. Ma and G. Marinescu, extit{Holomorphic Morse inequalities and Bergman kernels}, Progress in Math., vol. 254, Birkh$ddot{a}$user, Basel, 2007, 422 pp.
[5] D. Varolin, extit{Riemann Surfaces by Way of Complex Analytic Geometry}, 2011. |
指導教授 |
黃榮宗(Rung-Tzung Huang)
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審核日期 |
2017-7-12 |
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