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May
15
revised Proving Sard's theorem
added 901 characters in body
May
15
revised Proving Sard's theorem
added 255 characters in body
May
15
asked Proving Sard's theorem
May
14
revised If a composition of two maps is smooth, as well as one of the maps, then so is the other.
edited body
May
14
comment If a composition of two maps is smooth, as well as one of the maps, then so is the other.
Thank you, @ZhenLin. How can we proceed if all maps are surjective?
May
14
revised If a composition of two maps is smooth, as well as one of the maps, then so is the other.
edited body
May
14
asked The pullback bundle
May
14
asked If a composition of two maps is smooth, as well as one of the maps, then so is the other.
May
7
comment The inverse of a smooth bundle map is smooth.
Your suggestion helps me in part, @user86418. I see that smoothness of $\tilde f^{-1}$ implies smoothness of $f^{-1}$. Conversly, consider a point $b\in B_2$, a trivialization $x_2: P_2^{-1}(V)\to V\times F$ around $b$, and a trivialization $x_1:P_1^{-1}(U)\to U\times F$ around $f^{-1}(b)$. This gives us $P_1\circ x_1^{-1}\circ\tilde f^{-1}=f^{-1}\circ P_2\circ x_2^{-1}$. All the maps involved in the last identity are smooth except possibly $\tilde f^{-1}$. How can we conclude?
May
7
asked A differentiable fiber bundle exists for any family of clutching functions.
May
7
revised The inverse of a smooth bundle map is smooth.
added 942 characters in body
May
7
comment The inverse of a smooth bundle map is smooth.
I beg your pardon, @user86418, $\tilde f$ restricted to a fiber is not a diffeomorphism.
May
7
asked The inverse of a smooth bundle map is smooth.
Apr
29
asked The inverse image of any regular value is a submanifold
Apr
17
revised The curvatures of a transformed surface under a similarity transformation
Changed <> to \langle\rangle
Apr
17
accepted The curvatures of a transformed surface under a similarity transformation
Apr
17
revised The curvatures of a transformed surface under a similarity transformation
added 2 characters in body
Apr
17
comment The curvatures of a transformed surface under a similarity transformation
Thank you. I fixed the mistake from your second comment before I read your answer so I will not change it back. Still I do not see how to proceed with the mean curvature, nor how the Idea is useful.
Apr
17
revised The curvatures of a transformed surface under a similarity transformation
added 5 characters in body
Apr
17
revised The curvatures of a transformed surface under a similarity transformation
edited out balast