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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/94044

    Title: Morse theory to Reeb's theorem and its generalization
    Other Titles: Reeb定理上的Morse理論及其推廣
    Authors: 李容瑄;Lee, Jung-Hsuan
    Contributors: 淡江大學數學學系碩士班
    余成義;Yu, Cherng-Yih
    Keywords: Morse引理;Morse定理;Reeb定理;Morse lemma;Morse Theorem;Reeb's Therem
    Date: 2013
    Issue Date: 2014-01-23 13:49:32 (UTC+8)
    Abstract: 本文先介紹可微流型之定理及各種基本性質,也初略介紹具Riemann測度之可微流型。
    In this thesis, we want to use Morse Theorem to prove Reeb''s Theorem. Before showing the proof of these theorems, we need to review some basic properties of a differentiable manifold M with a differentiable structure. In general, if we define some functions from M (or its subspace) to real value, the difference between manifold and coordinate space should be considered. Every point we choose must send to a coordinate subspace first. So defining a coordinate system is helpful to deal with any functions on manifold M.
    The main result we review is to prove Reeb''s Theorem using Morse Lemma and Morse Theorem. Here we use a surgery lemma to prove disjoint union of two spaces, matched along their common boundary.
    We also show how to construct a homotopy equivalence between manifold M and a n-sphere, for all dimension n is larger or equal to 1.
    Appears in Collections:[數學學系暨研究所] 學位論文

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