Tagged Questions
0
votes
1answer
25 views
Prove this action is properly discontinuous..
Consider the group $\mathbb Z_2=\{0, 1\}$ acting on the sphere $\mathbb S^n$ through the group actions $\psi_0=Id$ e $\psi_1=-Id$. Show this actions is properly discontinuos? The definition of ...
2
votes
2answers
75 views
How to show $\mathbb R^n/\mathbb Z^n$ is diffeomorphic to torus $\mathbb T^n$?
Suppose the additive group $\mathbb Z^n$ acts on $\mathbb R^n$ through translation. How to show $\mathbb R^n/\mathbb Z^n$ is diffeomorphic to torus $\mathbb T^n$? The translation action is given by ...
1
vote
1answer
28 views
How to show the orbit space $\mathbb S^n/\mathbb Z_2$ is $\mathbb RP^n$?
How to show the orbit space $\mathbb S^n/\mathbb Z_2$ is $\mathbb RP^n$? Here $\mathbb Z_2=\{0, 1\}$ is the additive group and the group action considered induces the aplications $\psi_0=Id$ and ...
0
votes
0answers
44 views
Definition of g-orbit of a set
Let $g$ be a Lie algebra and $M$ a manifold, what does mean $g$-orbit of $M$?
2
votes
1answer
64 views
Hyperbolic spheres in the Poincare half-plane and fractional linaear transformations
Let $\mathbb{H}$ be the Poincare upper half-plane, seen as a
Riemannian manifold with the metric $$\frac{dx^2+dy^2}{y^2}.$$
Moreover, we consider the action of $\text{SL}_2(\mathbb{R})$ on
...
0
votes
0answers
80 views
Questions (doubts) on: Group Action on Manifolds
There are 2 questions that are bugging me in differential topology and I'd be glad if the same could be cleared up:
Let $X = x\frac{\partial}{\partial y}$ be a vector field on $M = R^2$, where $R$ ...
1
vote
0answers
36 views
A K-invariant submanifold of G-manifold and fundamental vector fields
Let a (connected) Lie group $G$ act on $M$. Assume that the action is locally free. (In other words, if the fundamental vector field of $X \in \mathrm{Lie(G)}$
$$
\underline{X}(p) := ...
