Skip to main content
MathOverflow

Return to Answer

Fixed spelling
Source Link
David White
David White
  • 30.3k
  • 9
  • 154
  • 250

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven:

Theorem. The quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomorfichomeomorphic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).

The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven:

Theorem. The quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomorfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).

The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven:

Theorem. The quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomorphic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).

The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).

Bounty Ended with 150 reputation awarded by Anton Petrunin
added 18 characters in body
Source Link
Dmitri Panov
Dmitri Panov
  • 28.9k
  • 4
  • 92
  • 161

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven that the quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomerfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i:

Theorem.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).The quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomorfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).

The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven that the quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomerfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2). The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven:

Theorem. The quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomorfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2).

The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).

Source Link
Dmitri Panov
Dmitri Panov
  • 28.9k
  • 4
  • 92
  • 161

In the following article of M.A.Mikhailova (М.А. Михайлова)

Изв. АН СССР. Сер. матем., 48:1 (1984)

О ФАКТОРПРОСТРАНСТВЕ ПО ДЕЙСТВИЮ КОНЕЧНОЙ ГРУППЫ, ПОРОЖДЕННОЙ ПСЕВДООТРАЖЕНИЯМИ.

http://www.mathnet.ru/links/33220b8c84645bec685e85bf17d65994/im1420.pdf

it is proven that the quotient $\mathbb R^n/G$ by a linear action of a finite group $G$ is homeomerfic to $\mathbb R^n$ if and only if $G$ is generated by pseudo-reflections (i.e, rotations of $\mathbb R^n$ that fix a subspace of codimension 2). The proof relies on a complete classification of finite groups generated by pseudo-reflections (there is a reference to this classification at the end of the article)

(there should be of course an English translation of this article, but I can not find it now).