| 词条 | Circle-valued Morse theory |
| 释义 |
In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold to the circle, in the framework of Morse homology.[1] It is an important special case of Sergei Novikov's Morse theory of closed one-forms.[2] Michael Hutchings and Yi-Jen Lee have connected it to Reidemeister torsion and Seiberg–Witten theory.[3]References1. ^{{citation | last = Pajitnov | first = Andrei V. | doi = 10.1515/9783110197976 | isbn = 978-3-11-015807-6 | mr = 2319639 | publisher = Walter de Gruyter & Co., Berlin | series = de Gruyter Studies in Mathematics | title = Circle-valued Morse theory | volume = 32 | year = 2006}}. {{topology-stub}}2. ^{{citation | last = Farber | first = Michael | doi = 10.1090/surv/108 | isbn = 0-8218-3531-9 | mr = 2034601 | page = 50 | publisher = American Mathematical Society, Providence, RI | series = Mathematical Surveys and Monographs | title = Topology of closed one-forms | url = https://books.google.com/books?hl=en&lr=&id=unm2pS8WiNsC&pg=PA50 | volume = 108 | year = 2004}}. 3. ^{{citation | last1 = Hutchings | first1 = Michael | authorlink = Michael Hutchings (mathematician) | last2 = Lee | first2 = Yi-Jen | doi = 10.1016/S0040-9383(98)00044-5 | issue = 4 | journal = Topology | mr = 1679802 | pages = 861–888 | title = Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds | volume = 38 | year = 1999| arxiv = dg-ga/9612004 }}. 1 : Morse theory |
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