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Title: On the normal subgroups of the group of volume preserving diffeomorphisms of Rⁿ for n ≥ 3
Author: de Sivera, Francisca Mascaro
ISNI:       0000 0001 3420 777X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1982
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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).
Supervisor: Not available Sponsor: Consejo Superior de Investigaciones Científicas (Spain)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics