簡易檢索 / 詳目顯示

研究生: 徐靖家
Hsu, Ching-Chia
論文名稱: 不變聯絡的無窮小量變化
Infinitesimal Variations of Invariant Connections
指導教授: 吳思曄
Wu, Siye
口試委員: 何南國
Ho, Nan-Kou
鄭日新
Cheng, Jih-Hsin
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2022
畢業學年度: 110
語文別: 英文
論文頁數: 23
中文關鍵詞: 不變聯絡李代數的上同調
外文關鍵詞: Invariant connections, Lie algebra cohomology
相關次數: 點閱:4下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 本論文藉由擾動不變聯絡得到一個李代數上鏈餘鏈複體,並透過懷特海德的定理 計算其指標。


    In this work we obtain a Lie algebra cochain complex via variating the invariant connections infinitesimally, and compute its index by using Whiteheads Theorem.

    1. Introduction 2 2. Preliminaries 3 3. Invariant connections and Wang’s theorem 6 4. Infinitesimal variations of invariant connections 15

    [CE48] Claude Chevalley and Samuel Eilenberg. Cohomology theory of lie groups and lie algebras. Transactions of the American Mathematical society, 63(1):85–124, 1948.
    [HSV80] John Harnad, Steven Shnider, and Luc Vinet. Group actions on principal bundles and invariance conditions for gauge fields. Journal of Mathematical Physics, 21(12):2719–2724, 1980.
    [KN63]Kobayashi Kobayashi and Katsumi Nomizu. Foundations of differential geometry I. John Wiley and Sons, 1963.
    [Lyo03] D. Lyons. An Elementary Introduction to the Hopf Fibration, volume 76(2). Mathematics Magazine, 2003.
    [PR09]Dennis The. Invariant yang– mills connections over non-reductive pseudo-riemannian homogeneous spaces. AMERICAN MATHEMATICAL SOCIETY, 361(7):3879–3914, 2009.
    [TU18]LORING W. TU. Differential geometry: Connections, curvature, and characteristic classes. SPRINGER INTERNATIONAL PU, 2018.
    [Wan49]Hsien-Chung Wang. Homogeneous spaces with non-vanishing euler char- acteristics. Annals of Mathematics, pages 925–953, 1949.
    [Wan58] Hsien-chung Wang. On invariant connections over a principal fibre bundle.
    Nagoya Mathematical Journal, 13:1–19, 1958.

    QR CODE