Normal subgroups of $\textrm {Diff}^{\Omega }(\textbf {R}^{3})$
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- by Francisca Mascaró
- Proc. Amer. Math. Soc. 92 (1984), 609-614
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760953-X
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Abstract:
Let $\Omega$ be a volume element on ${{\mathbf {R}}^3}$ of infinite total $\Omega$-volume. We denote by ${\operatorname {Dif}}{{\text {f}}^\Omega }({{\mathbf {R}}^3})$ the group of all $\Omega$-preserving diffeomorphisms of ${{\mathbf {R}}^3}$, by ${\operatorname {Diff}}_{\text {c}}^\Omega ({{\mathbf {R}}^3})$ the subgroup of all elements with compact support and by ${\operatorname {Diff}}_{\text {f}}^{\Omega }(\mathbf {R}^3)$ the subgroup of all elements whose support has finite $\Omega$-volume. We prove that there is no normal subgroup between ${\operatorname {Diff}}_{\text {c}}^\Omega ({{\mathbf {R}}^3})$ and ${\operatorname {Diff}}_{\text {f}}^\Omega ({{\mathbf {R}}^3})$.References
- Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Ginn and Company, Boston, Mass., 1963. Based upon lectures given at Haverford College under the Philips Lecture Program. MR 0146828
- D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math. 22 (1970), 165–173. MR 267589
- R. E. Greene and K. Shiohama, Diffeomorphisms and volume-preserving embeddings of noncompact manifolds, Trans. Amer. Math. Soc. 255 (1979), 403–414. MR 542888, DOI 10.1090/S0002-9947-1979-0542888-3
- A. B. Krygin, Extension of diffeomorphisms that preserve volume, Funkcional. Anal. i Priložen. 5 (1971), no. 2, 72–76 (Russian). MR 0368067
- Francisca Mascaró, Normal subgroups of $\textrm {Diff}^{\Omega }(\textbf {R}^{n})$, Trans. Amer. Math. Soc. 275 (1983), no. 1, 163–173. MR 678342, DOI 10.1090/S0002-9947-1983-0678342-9
- Dusa McDuff, On the group of volume-preserving diffeomorphisms of $\textbf {R}^{n}$, Trans. Amer. Math. Soc. 261 (1980), no. 1, 103–113. MR 576866, DOI 10.1090/S0002-9947-1980-0576866-3
- Dusa McDuff, On groups of volume-preserving diffeomorphisms and foliations with transverse volume form, Proc. London Math. Soc. (3) 43 (1981), no. 2, 295–320. MR 628279, DOI 10.1112/plms/s3-43.2.295
- Dusa McDuff, On tangle complexes and volume-preserving diffeomorphisms of open $3$-manifolds, Proc. London Math. Soc. (3) 43 (1981), no. 2, 321–333. MR 628280, DOI 10.1112/plms/s3-43.2.321
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 609-614
- MSC: Primary 58D05; Secondary 57R50
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760953-X
- MathSciNet review: 760953