Yau, Sin Wa. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 78-80). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Morse Theory --- p.3 / Chapter 2.1 --- Definition --- p.3 / Chapter 2.2 --- Existence of Morse functions --- p.4 / Chapter 2.3 --- Properties of Morse functions --- p.7 / Chapter 2.4 --- The Morse homology --- p.16 / Chapter 2.4.1 --- Counting the number of flow lines with sign --- p.18 / Chapter 2.4.2 --- The Morse complex and the Morse homology --- p.19 / Chapter 2.5 --- The Morse inequality --- p.27 / Chapter 3 --- The Novikov homology --- p.29 / Chapter 3.1 --- The Novikov complex --- p.29 / Chapter 3.2 --- Relates the Novikov homology to the singular homology --- p.39 / Chapter 3.3 --- Properties of the Novikov homology --- p.43 / Chapter 3.4 --- The Novikov inequality and some applications --- p.51 / Chapter 4 --- Comparion with classical Morse theory --- p.55 / Chapter 5 --- Applications to knots and links --- p.58 / Chapter 5.1 --- Regular Morse functions --- p.58 / Chapter 5.2 --- The Morse-Novikov number --- p.74 / Chapter 5.3 --- The Universal Novikov homology --- p.76 / Bibliography --- p.78
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326865 |
| Date | January 2009 |
| Contributors | Yau, Sin Wa., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, v, 80 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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