Mixing
Exponential map is smooth
$begingroup$
Let $G$ be a lie group, then it is claimed that the exponential map
$$exp: Lie(G) rightarrow G$$
is a smooth map. I want to know - what is the smooth structure of $Lie(G)$?
I am supposing it is identified with $T_eG$ and we show that $T_eG$ is an embedded submanifold of $TG$.
differential-geometry lie-groups lie-algebras
asked Jan 21 at 10:56
CL.CL.
2,3042925
$endgroup$
add a comment |
$begingroup$
Let $G$ be a lie group, then it is claimed that the exponential map
$$exp: Lie(G) rightarrow G$$
is a smooth map. I want to know - what is the smooth structure of $Lie(G)$?
I am supposing it is identified with $T_eG$ and we show that $T_eG$ is an embedded submanifold of $TG$.
differential-geometry lie-groups lie-algebras
asked Jan 21 at 10:56
CL.CL.
2,3042925
$endgroup$
2
$begingroup$
There is a canonical smooth structure on any finite-dimensional (real) vector space described here: math.stackexchange.com/questions/160298/…
$endgroup$
– MaoWao
Jan 21 at 12:31
add a comment |
$begingroup$
Let $G$ be a lie group, then it is claimed that the exponential map
$$exp: Lie(G) rightarrow G$$
is a smooth map. I want to know - what is the smooth structure of $Lie(G)$?
I am supposing it is identified with $T_eG$ and we show that $T_eG$ is an embedded submanifold of $TG$.
differential-geometry lie-groups lie-algebras
asked Jan 21 at 10:56
CL.CL.
2,3042925
$endgroup$
Let $G$ be a lie group, then it is claimed that the exponential map
$$exp: Lie(G) rightarrow G$$
is a smooth map. I want to know - what is the smooth structure of $Lie(G)$?
I am supposing it is identified with $T_eG$ and we show that $T_eG$ is an embedded submanifold of $TG$.
differential-geometry lie-groups lie-algebras
differential-geometry lie-groups lie-algebras
asked Jan 21 at 10:56
CL.CL.
2,3042925
asked Jan 21 at 10:56
CL.CL.
2,3042925
asked Jan 21 at 10:56
CL.CL.
2,3042925
asked Jan 21 at 10:56
CL.CL.
2,3042925
asked Jan 21 at 10:56
CL.CL.
2,3042925
2,3042925
2
$begingroup$
There is a canonical smooth structure on any finite-dimensional (real) vector space described here: math.stackexchange.com/questions/160298/…
$endgroup$
– MaoWao
Jan 21 at 12:31
add a comment |
2
$begingroup$
There is a canonical smooth structure on any finite-dimensional (real) vector space described here: math.stackexchange.com/questions/160298/…
$endgroup$
– MaoWao
Jan 21 at 12:31
2
2
$begingroup$
There is a canonical smooth structure on any finite-dimensional (real) vector space described here: math.stackexchange.com/questions/160298/…
$endgroup$
– MaoWao
Jan 21 at 12:31
$begingroup$
There is a canonical smooth structure on any finite-dimensional (real) vector space described here: math.stackexchange.com/questions/160298/…
$endgroup$
– MaoWao
Jan 21 at 12:31
add a comment |
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$begingroup$
There is a canonical smooth structure on any finite-dimensional (real) vector space described here: math.stackexchange.com/questions/160298/…
$endgroup$
– MaoWao
Jan 21 at 12:31