Question

Why can't we define the pushforward $T_x(f)v$ to be ${\rm D}\tilde f(x)v$, where $\tilde f$ is any $C^1$-extension of $f$?

score 55 · Answer 1 · 2020-09-09 15:15:12

55

Views

Why can't we define the pushforward $T_x(f)v$ to be ${\rm D}\tilde f(x)v$, where $\tilde f$ is any $C^1$-extension of $f$?

Published on 09 Sep 2020 - 15:15

score 73 · Answer 2 · 2020-09-11 19:23:02

73

Views

If $M_i$ is a submanifold with $M_1\subseteq M_2$, what's the pushforward of the restriction $\left.f\right|_{M_1}$ of a map $f:M_2\to\mathbb R$?

Published on 11 Sep 2020 - 19:23

score 66 · Answer 3 · 2020-09-18 19:02:57

66

Views

How do we need to apply the chain rule to obtain this identity for the material derivative?

Published on 18 Sep 2020 - 19:02

score 6.7k · Answer 4 · 2020-09-21 15:18:58

6.7k

Views

Basic Confusion on Push-Forward of a Measure

Published on 21 Sep 2020 - 15:18

score 341 · Answer 5 · 2020-09-22 13:11:36

341

Views

Entropy of a Probability Measure after Push-forward

Published on 22 Sep 2020 - 13:11

score 42 · Answer 6 · 2020-09-25 15:31:45

42

Views

Show that for two vector spaces, $dF_p(X) = \lim_{t\to 0}(F(p+tX)-F(p))/t$.

Published on 25 Sep 2020 - 15:31

score 91 · Answer 7 · 2020-10-01 05:07:01

91

Views

Why is this application of the chain rule for the pushforward well-defined?

Published on 01 Oct 2020 - 5:07

score 1.1k · Answer 8 · 2026-02-24 01:42:57

1.1k

Views

rank and degree of vector bundle after push-forward or pull-back

Published on 24 Feb 2026 - 1:42

score 113 · Answer 9 · 2020-10-11 08:25:00

113

Views

Can we form a topological or Banach space of $C^1$-differentiable functions on a manifold?

Published on 11 Oct 2020 - 8:25

score 607 · Answer 10 · 2020-11-14 08:39:42

607

Views

Push-forward of vector fields over smooth manifolds

Published on 14 Nov 2020 - 8:39

score 215 · Answer 11 · 2020-11-14 23:35:55

215

Views

Pushforward Lorentz metric: $ds^2=dxdy $

Published on 14 Nov 2020 - 23:35

score 599 · Answer 12 · 2020-12-14 17:58:37

599

Views

Push Forwards and Change of Variable Confusion

Published on 14 Dec 2020 - 17:58

score 671 · Answer 13 · 2020-12-22 19:50:22

671

Views

Calculating the Fundamental Group of a CW Complex with Attaching Maps of Varying Degrees

Published on 22 Dec 2020 - 19:50

score 117 · Answer 14 · 2026-02-24 01:43:14

117

Views

Doubt showing commutativity of Pushforward and Lie Bracket

Published on 24 Feb 2026 - 1:43

score 113 · Answer 15 · 2020-12-30 07:35:04

113

Views

Constructing a measure space given the definition of a measurable function

Published on 30 Dec 2020 - 7:35

List Question

Why can't we define the pushforward $T_x(f)v$ to be ${\rm D}\tilde f(x)v$, where $\tilde f$ is any $C^1$-extension of $f$?

If $M_i$ is a submanifold with $M_1\subseteq M_2$, what's the pushforward of the restriction $\left.f\right|_{M_1}$ of a map $f:M_2\to\mathbb R$?

How do we need to apply the chain rule to obtain this identity for the material derivative?

Basic Confusion on Push-Forward of a Measure

Entropy of a Probability Measure after Push-forward

Show that for two vector spaces, $dF_p(X) = \lim_{t\to 0}(F(p+tX)-F(p))/t$.

Why is this application of the chain rule for the pushforward well-defined?

rank and degree of vector bundle after push-forward or pull-back

Can we form a topological or Banach space of $C^1$-differentiable functions on a manifold?

Push-forward of vector fields over smooth manifolds

Pushforward Lorentz metric: $ds^2=dxdy $

Push Forwards and Change of Variable Confusion

Calculating the Fundamental Group of a CW Complex with Attaching Maps of Varying Degrees

Doubt showing commutativity of Pushforward and Lie Bracket

Constructing a measure space given the definition of a measurable function

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