On admissible groups of diffeomorphisms

Rybicki, Tomasz. "On admissible groups of diffeomorphisms." Proceedings of the 16th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1997. [139]-146. <http://eudml.org/doc/221331>.

@inProceedings{Rybicki1997,
abstract = {The phenomenon of determining a geometric structure on a manifold by the group of its automorphisms is a modern analogue of the basic ideas of the Erlangen Program of F. Klein. The author calls such diffeomorphism groups admissible and he describes them by imposing some axioms. The main result is the followingTheorem. Let $(M_i, \alpha _i)$, $i= 1,2$, be a geometric structure such that its group of automorphisms $G(M_i, \alpha _i)$ satisfies either axioms 1, 2, 3 and 4, or axioms 1, 2, 3’, 4, 5, 6 and 7, and $M_i$ is compact, or axioms 1, 2, 3’, 4, 5, 6, 7, 8 and 9. Then if there is a group isomorphism $\Phi : G(M_1, \alpha _1) \rightarrow G(M_2, \alpha _2)$ then there is a unique $C^\infty $-diffeomorphism $\varphi : M_1\rightarrow M_2$ preserving $\alpha _i$ and such that $\Phi (f) =\varphi f\varphi ^\{-1\}$ for each $f\in G(M_1, \alpha _1)$. The axioms referred to in the theorem concern a finite open cover of $\text\{supp\} (f)$, $\text\{Fix\} (f)$, leaves of a generalization folia!},
author = {Rybicki, Tomasz},
booktitle = {Proceedings of the 16th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Srní (Czech Republic); Geometry; Physics},
location = {Palermo},
pages = {[139]-146},
publisher = {Circolo Matematico di Palermo},
title = {On admissible groups of diffeomorphisms},
url = {http://eudml.org/doc/221331},
year = {1997},
}

TY - CLSWK
AU - Rybicki, Tomasz
TI - On admissible groups of diffeomorphisms
T2 - Proceedings of the 16th Winter School "Geometry and Physics"
PY - 1997
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [139]
EP - 146
AB - The phenomenon of determining a geometric structure on a manifold by the group of its automorphisms is a modern analogue of the basic ideas of the Erlangen Program of F. Klein. The author calls such diffeomorphism groups admissible and he describes them by imposing some axioms. The main result is the followingTheorem. Let $(M_i, \alpha _i)$, $i= 1,2$, be a geometric structure such that its group of automorphisms $G(M_i, \alpha _i)$ satisfies either axioms 1, 2, 3 and 4, or axioms 1, 2, 3’, 4, 5, 6 and 7, and $M_i$ is compact, or axioms 1, 2, 3’, 4, 5, 6, 7, 8 and 9. Then if there is a group isomorphism $\Phi : G(M_1, \alpha _1) \rightarrow G(M_2, \alpha _2)$ then there is a unique $C^\infty $-diffeomorphism $\varphi : M_1\rightarrow M_2$ preserving $\alpha _i$ and such that $\Phi (f) =\varphi f\varphi ^{-1}$ for each $f\in G(M_1, \alpha _1)$. The axioms referred to in the theorem concern a finite open cover of $\text{supp} (f)$, $\text{Fix} (f)$, leaves of a generalization folia!
KW - Proceedings; Winter school; Srní (Czech Republic); Geometry; Physics
UR - http://eudml.org/doc/221331
ER -