bio | website | poisson.dm.unipi.it/~monge |
---|---|---|
location | Pisa (Italy) | |
age | 32 | |
visits | member for | 4 years, 5 months |
seen | May 22 at 1:03 | |
stats | profile views | 616 |
Jul 2 |
awarded | Curious |
Feb 25 |
comment |
Is a left topological group which is a manifold a topological group?
That the idea does not work "as is" with $H=K$, where I was looking for a non-continuous $H\rightarrow{}K$ that could then be composed with the canonical $K\rightarrow{}Inn(K)$. But actually I just realized that this can work very easily with $S^1$ and $SO(2)$, considering an isomorphical embedding $S^1\rightarrow{}SO(2)$ and a non-continuous homomorphism $S^1\rightarrow{}S^1$ (which exists). In this way we easily have a non-continuous homomorphism $S^1\rightarrow{}Aut(SO(2))$, and a similar example (that is also compact). |
Feb 24 |
comment |
Is a left topological group which is a manifold a topological group?
It is interesting to point out that the same example cannot work with compact semisimple Lie groups (replacing $xe^{f(y)}$ with the conjugacy $yxy^{-1}$, that sends as well $G\rightarrow{}Inn(G)\subseteq{}Aut(G)$), because in this case any automorphism is automatically continuous, as pointed out in mathoverflow.net/a/40700/3680 |
Feb 24 |
revised |
Is a left topological group which is a manifold a topological group?
added 111 characters in body |
Feb 24 |
comment |
Is a left topological group which is a manifold a topological group?
Nice example, thanks! |
Feb 24 |
accepted | Is a left topological group which is a manifold a topological group? |
Feb 23 |
comment |
Is a left topological group which is a manifold a topological group?
yes, let's also assume $G$ paracompact, with countable atlas as topological manifold. @GeraldEdgar nice theorem, even if I don't see an immediate application to the present case, what is a reference for it? |
Feb 22 |
awarded | Nice Question |
Feb 22 |
revised |
Is a left topological group which is a manifold a topological group?
added 195 characters in body |
Feb 22 |
comment |
Is a left topological group which is a manifold a topological group?
I see... thanks, if you write it as an answer I will accept it. In any case, I was not thinking about this kind of examples, I think I should add that $G$ is supposed to be connected. |
Feb 22 |
comment |
Is a left topological group which is a manifold a topological group?
If you make the coset of a a one-parameter subgroup open (and hence also closed), how can the group still be a topological manifold? |
Feb 21 |
asked | Is a left topological group which is a manifold a topological group? |
Jan 27 |
answered | Ergodicity of composition with a rotation |
Oct 29 |
awarded | Nice Answer |
Oct 11 |
comment |
A Differential Equation with Nested Functions
can you provide some background? |
May 12 |
awarded | Popular Question |
Jan 31 |
awarded | Yearling |
May 16 |
comment |
about the local ring of $\mathbb{Z}_p[T]/(pT^2+T+1)$ at the prime p
Another way to see immediately that the equation has a solution is via Newton's polygon: it is formed by two sides with slopes 0 and 1, and each corresponds to a non-trivial factor, having degree 1. |
Feb 1 |
awarded | Yearling |
Jan 9 |
comment |
Examples of “Monster” groups
Perhaps their presentation is not the best way to understand them, in any case. |