Gelfand–Fuks cohomology: Difference between revisions
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== References == |
== References == |
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* I. |
*{{cite journal |last=Gel'fand |first=I.M. |last2=Fuks |first2=D.B. |title=Cohomologies of Lie algebra of tangential vector fields of a smooth manifold |journal=Funct Anal Its Appl |volume=3 |pages=194–210 |year=1969 |doi=10.1007/BF01676621 }} |
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* I. |
*{{cite journal |last=Gel'fand |first=I.M. |last2=Fuks |first2=D.B. |title=Cohomologies of Lie algebra of tangential vector fields. II |journal=Funct Anal Its Appl |volume=4 |pages=110–6 |year=1970 |doi=10.1007/BF01094486 }} |
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*{{cite journal |last=Gel'fand |first=I.M. |last2=Fuks |first2=D.B. |title=The cohomology of the Lie algebra of formal vector fields |journal=Mathematics of the USSR-Izvestiya |volume=2 |issue=2 |pages=327–342 |year=1970 |doi=10.1070/im1970v004n02abeh000908 }} |
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*{{cite book |author=Shigeyuki Morita |chapter=§2.4 Gel'fand–Fuks cohomology |title=Geometry of Characteristic Classes |chapterurl=https://books.google.com/books?id=8n1mAwAAQBAJ&pg=PA75 |year=2001 |publisher=American Mathematical Society |volume=199 |series=Translations of Mathematical Monographs |isbn=978-0-8218-2139-8 |pages=75–}} |
*{{cite book |author=Shigeyuki Morita |chapter=§2.4 Gel'fand–Fuks cohomology |title=Geometry of Characteristic Classes |chapterurl=https://books.google.com/books?id=8n1mAwAAQBAJ&pg=PA75 |year=2001 |publisher=American Mathematical Society |volume=199 |series=Translations of Mathematical Monographs |isbn=978-0-8218-2139-8 |pages=75–}} |
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Revision as of 11:49, 5 May 2020
In mathematics, Gelfand–Fuks cohomology, introduced in (Gelfand & Fuks 1969–70), is a cohomology theory for Lie algebras of smooth vector fields. It differs from the Lie algebra cohomology of Chevalley-Eilenberg in that its cochains are taken to be continuous multilinear alternating forms on the Lie algebra of smooth vector fields where the latter is given the topology.
References
- Gel'fand, I.M.; Fuks, D.B. (1969). "Cohomologies of Lie algebra of tangential vector fields of a smooth manifold". Funct Anal Its Appl. 3: 194–210. doi:10.1007/BF01676621.
- Gel'fand, I.M.; Fuks, D.B. (1970). "Cohomologies of Lie algebra of tangential vector fields. II". Funct Anal Its Appl. 4: 110–6. doi:10.1007/BF01094486.
- Gel'fand, I.M.; Fuks, D.B. (1970). "The cohomology of the Lie algebra of formal vector fields". Mathematics of the USSR-Izvestiya. 2 (2): 327–342. doi:10.1070/im1970v004n02abeh000908.
- Shigeyuki Morita (2001). "§2.4 Gel'fand–Fuks cohomology". Geometry of Characteristic Classes. Translations of Mathematical Monographs. Vol. 199. American Mathematical Society. pp. 75–. ISBN 978-0-8218-2139-8.
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Further reading
- Gelfand–Fuks cohomology at the nLab