Mixing
Criterion for pullback to be a manifold
$begingroup$
Suppose we have a smooth map $F:Mrightarrow N$ and a map $G:Urightarrow N$. We can talk about pullback $Mtimes_NU$ as a set given by ${(m,u):F(m)=G(u)}$.
Suppose $F$ or $G$ is a submersion, then $Mtimes_N U$ is a smooth manifold. We do not have that for us.
What we have is :
For some open cover ${U_alpha}$ of $U$, the pullbacks $Mtimes_N U_alpha$ are manifolds. Does it imply $Mtimes_N U$ is a manifold?
differential-geometry smooth-manifolds pullback
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
$endgroup$
add a comment |
$begingroup$
Suppose we have a smooth map $F:Mrightarrow N$ and a map $G:Urightarrow N$. We can talk about pullback $Mtimes_NU$ as a set given by ${(m,u):F(m)=G(u)}$.
Suppose $F$ or $G$ is a submersion, then $Mtimes_N U$ is a smooth manifold. We do not have that for us.
What we have is :
For some open cover ${U_alpha}$ of $U$, the pullbacks $Mtimes_N U_alpha$ are manifolds. Does it imply $Mtimes_N U$ is a manifold?
differential-geometry smooth-manifolds pullback
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
$endgroup$
add a comment |
$begingroup$
Suppose we have a smooth map $F:Mrightarrow N$ and a map $G:Urightarrow N$. We can talk about pullback $Mtimes_NU$ as a set given by ${(m,u):F(m)=G(u)}$.
Suppose $F$ or $G$ is a submersion, then $Mtimes_N U$ is a smooth manifold. We do not have that for us.
What we have is :
For some open cover ${U_alpha}$ of $U$, the pullbacks $Mtimes_N U_alpha$ are manifolds. Does it imply $Mtimes_N U$ is a manifold?
differential-geometry smooth-manifolds pullback
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
$endgroup$
Suppose we have a smooth map $F:Mrightarrow N$ and a map $G:Urightarrow N$. We can talk about pullback $Mtimes_NU$ as a set given by ${(m,u):F(m)=G(u)}$.
Suppose $F$ or $G$ is a submersion, then $Mtimes_N U$ is a smooth manifold. We do not have that for us.
What we have is :
For some open cover ${U_alpha}$ of $U$, the pullbacks $Mtimes_N U_alpha$ are manifolds. Does it imply $Mtimes_N U$ is a manifold?
differential-geometry smooth-manifolds pullback
differential-geometry smooth-manifolds pullback
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
asked Jan 2 at 11:24
Praphulla KoushikPraphulla Koushik
26917
26917
add a comment |
add a comment |
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