Riemann-Roch-Hirzebruch Theorem For Circle Bundle Over A Riemann Surface

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廖欣瑩(Sin-Ying Liao) 查詢紙本館藏

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論文名稱

(Riemann-Roch-Hirzebruch Theorem For Circle Bundle Over A Riemann Surface)

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★ Witten Deformation and Morse Inequalities	★ 射影變換群之探討
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★ Asymptotics of the Bergman Kernel for Positive Line Bundles	★ Lefschetz Fixed Point Formula on Absolute and Relative de Rham Complexes
★ Product Formula for Analytic Torsion on CR manifolds with S^1-action

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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)

審核日期

2017-7-12

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