bio | website | poisson.dm.unipi.it/~monge |
---|---|---|
location | Pisa (Italy) | |
age | 33 | |
visits | member for | 4 years, 9 months |
seen | Oct 23 at 2:53 | |
stats | profile views | 632 |
Sep 8 |
comment |
Help with my research topic
By the way, don't feel afraid to change advisor (either formally, either "de facto"). If after two years you are not being helped in any way to get in touch with current research problems don't make the mistake (that I did) to think that your best opportunity is trying to make your current setup work at all costs. Getting in touch with the state of the art in a research field is hard, you should have someone you can question about it. |
Aug 22 |
asked | Extension of the product formula for valuations to a simultaneous completion |
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. |