604 reputation
413
bio website poisson.dm.unipi.it/~monge
location Pisa (Italy)
age 32
visits member for 4 years, 2 months
seen Mar 17 at 17:45

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.
Jan
9
accepted Is a profinite group with a finite number of simple quotients and Jordan-Hölder factors finitely generated?