Normal bundle to $Z$ in $Y$ is a manifold with same dimension as $Y$ (Exercise 2.3.12 of Guillemin-Pollack)
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Here we have $l > k$. I let $phi : U times mathbb R^l longrightarrow N(Z;mathbb R^M)$ be the associated parametrization. I thought that to restrict $U times mathbb R^l$ to $U times mathbb R^k$ one should consider the projection map $pi : U times mathbb R^l longrightarrow U times mathbb R^k$. I'm not sure how that helps though, because I thought I needed to prove that the restricted parametrization $pivert_{U times mathbb R^k}$ maps $U times mathbb R^k$ onto $N(Z;Y)$.
differential-topology
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Here we have $l > k$. I let $phi : U times mathbb R^l longrightarrow N(Z;mathbb R^M)$ be the associated parametrization. I thought that to restrict $U times mathbb R^l$ to $U times mathbb R^k$ one should consider the projection map $pi : U times mathbb R^l longrightarrow U times mathbb R^k$. I'm not sure how that helps though, because I thought I needed to prove that the restricted parametrization $pivert_{U times mathbb R^k}$ maps $U times mathbb R^k$ onto $N(Z;Y)$.
differential-topology
asked yesterday
Cookie
8,677123479
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Here we have $l > k$. I let $phi : U times mathbb R^l longrightarrow N(Z;mathbb R^M)$ be the associated parametrization. I thought that to restrict $U times mathbb R^l$ to $U times mathbb R^k$ one should consider the projection map $pi : U times mathbb R^l longrightarrow U times mathbb R^k$. I'm not sure how that helps though, because I thought I needed to prove that the restricted parametrization $pivert_{U times mathbb R^k}$ maps $U times mathbb R^k$ onto $N(Z;Y)$.
differential-topology
asked yesterday
Cookie
8,677123479
Here we have $l > k$. I let $phi : U times mathbb R^l longrightarrow N(Z;mathbb R^M)$ be the associated parametrization. I thought that to restrict $U times mathbb R^l$ to $U times mathbb R^k$ one should consider the projection map $pi : U times mathbb R^l longrightarrow U times mathbb R^k$. I'm not sure how that helps though, because I thought I needed to prove that the restricted parametrization $pivert_{U times mathbb R^k}$ maps $U times mathbb R^k$ onto $N(Z;Y)$.
differential-topology
differential-topology
asked yesterday
Cookie
8,677123479
asked yesterday
Cookie
8,677123479
asked yesterday
Cookie
8,677123479
asked yesterday
Cookie
8,677123479
asked yesterday
Cookie
8,677123479
8,677123479
add a comment |
add a comment |
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