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On the normal subgroups of the group of volume preserving diffeomorphisms of R[sup]n for n≥3
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Sivera, Francisca Mascaro de (1982) On the normal subgroups of the group of volume preserving diffeomorphisms of R[sup]n for n≥3. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3253368~S15
Abstract
Let Ώ be a volume element on Rn.Diff Ώ (Rn) is the
group of Ώ -preserving diffeomorphisms of Rn. Diff Ώw(Rn) is the subgroup of all elements whose set of non-fixed points has finite Ώ-volume. Diff Ώc(Rn) is the subgroup of all elements whose support has finite «-volume. Diff Ώf(Fn) is the subgroup of all elements with compact support. Diff Ώco(Rn) is the subgroup of all elements compactly «-isotopic to the identity.
We prove, in case volΏn < 00 and for n >, 3,
that a subgroup of Diff Ώ(Rn) , N , is normal if and only if Diff Ώco(Rn) c N c Diff Ώ(Rn). If volΏ Rn = 00 and for n > 3 , there is no normal subgroup neither between Diff Ώw(Rn) and DiffV(Rn) nor between DiffΏc(Rn) and DiffΏf (Rn).
| Item Type: | Thesis (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Diffeomorphisms | ||||
| Official Date: | September 1982 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Rourke, C. P. (Colin Patrick), 1943- | ||||
| Sponsors: | Consejo Superior de Investigaciones Científicas (Spain) | ||||
| Format of File: | |||||
| Extent: | v, 115 leaves :|billustrations | ||||
| Language: | eng |
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