List questions from differential-topology

Published on 10 Apr 2026 - 12:01

1.1k

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Show $f^*dx_i = \sum_{j=1}^l \frac{\partial f_i}{\partial y_j} dy_j = df_i$

Published on 12 Apr 2026 - 21:46

124

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$f^(w_1 + w_2) = f^w_1 + f^* w_2$

Published on 17 Apr 2026 - 15:08

140

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$(f\circ h)^* \omega = h^f^\omega$ - Legit now?

Published on 12 Apr 2026 - 1:53

74

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Linearity of everything

Published on 09 Apr 2026 - 22:21

250

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Linearity of $f_, f^$.

Published on 16 Apr 2026 - 10:17

1.3k

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Linearity of push forward $F_*$

Published on 15 Apr 2026 - 12:48

816

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Define pull-back on a manifold by pull-back on the linear space.

Published on 14 Apr 2026 - 17:31

409

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Textbooks with exposition done mostly in proof outlines or exercises?

Published on 15 Apr 2026 - 22:30

72

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Abbreviation of volumn form

Published on 10 Apr 2026 - 20:04

1.7k

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Change of Variable vs. Change of Coordinates.

Published on 14 Apr 2026 - 15:32

1k

Views

The Generalized Stokes Theorem.

Published on 13 Apr 2026 - 22:13

435

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Winding number of $f$ is equal to $\frac{1}{2\pi}\int_{S^1}f^*(d\theta).$

Published on 15 Apr 2026 - 19:22

77

Views

Problem reduced to analyzing solutions of a family of nonlinear systems of equations

Published on 10 Apr 2026 - 21:01

104

Views

Why can an orientation on $X$ be written as a sum of cycles on this open cover?

Published on 13 Apr 2026 - 0:52

List Question

About zeros of vector fields in compact surfaces

Show $f^*dx_i = \sum_{j=1}^l \frac{\partial f_i}{\partial y_j} dy_j = df_i$

$f^(w_1 + w_2) = f^w_1 + f^* w_2$

$(f\circ h)^* \omega = h^f^\omega$ - Legit now?

Linearity of everything

Linearity of $f_, f^$.

Linearity of push forward $F_*$

Define pull-back on a manifold by pull-back on the linear space.

Textbooks with exposition done mostly in proof outlines or exercises?

Abbreviation of volumn form

Change of Variable vs. Change of Coordinates.

The Generalized Stokes Theorem.

Winding number of $f$ is equal to $\frac{1}{2\pi}\int_{S^1}f^*(d\theta).$

Problem reduced to analyzing solutions of a family of nonlinear systems of equations

Why can an orientation on $X$ be written as a sum of cycles on this open cover?

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