Question

Show that the index of $r$ must be the sum of the indices of $p$ and $q$.

score 75 · Answer 1 · 2026-04-15 14:47:01

75

Views

Show that the index of $r$ must be the sum of the indices of $p$ and $q$.

Published on 15 Apr 2026 - 14:47

score 332 · Answer 2 · 2026-04-11 11:14:52

332

Views

submanifold and open subset

Published on 11 Apr 2026 - 11:14

score 143 · Answer 3 · 2026-04-12 22:52:39

143

Views

How can I show that $a,b \in Z$?

Published on 12 Apr 2026 - 22:52

score 33 · Answer 4 · 2026-04-16 03:38:20

33

Views

The solution set in $\mathbb{R}^3 - \{0\}$ of $x^d +y^d= z^d$ has the form $p^{-1}(X_d)$.

Published on 16 Apr 2026 - 3:38

score 268 · Answer 5 · 2026-03-26 14:18:42

268

Views

Non degenerate critical points.

Published on 26 Mar 2026 - 14:18

score 156 · Answer 6 · 2026-04-14 17:51:17

156

Views

What is $g$ in Guillemin and Pollack's Differential Topology?

Published on 14 Apr 2026 - 17:51

score 109 · Answer 7 · 2026-04-10 20:22:20

109

Views

$f: X \to Y$ is a submersion, $X$ is compact and $Y$ is connected - why $f(X)$ is open?

Published on 10 Apr 2026 - 20:22

score 1.4k · Answer 8 · 2026-04-15 21:55:27

1.4k

Views

Projection, canonical immersion/submersion - are they equivalent, and are they open maps?

Published on 15 Apr 2026 - 21:55

score 246 · Answer 9 · 2026-04-12 11:27:09

246

Views

How to draw the conclusion that $f$ is continuous?

Published on 12 Apr 2026 - 11:27

score 1.6k · Answer 10 · 2026-04-14 14:29:20

1.6k

Views

The independence of gradient.

Published on 14 Apr 2026 - 14:29

score 527 · Answer 11 · 2026-04-15 12:38:41

527

Views

GP 1.4.4 An extension of partial converse of preimage theorem.

Published on 15 Apr 2026 - 12:38

score 77 · Answer 12 · 2026-04-14 15:48:43

77

Views

$\mathbb{R}^k$ and $\mathbb{R}^k$ are trivially diffeomorphic.

Published on 14 Apr 2026 - 15:48

score 61 · Answer 13 · 2026-03-26 14:17:18

61

Views

Finite approximation of path space.

Published on 26 Mar 2026 - 14:17

score 912 · Answer 14 · 2026-03-26 11:01:12

912

Views

If $p$ is homogeneous of order $k$, then $p^{-1}(a)$ is diffeomorphic to $p^{-1}(b)$

Published on 26 Mar 2026 - 11:01

score 182 · Answer 15 · 2026-04-11 11:14:34

182

Views

studying compact $\partial$-$n$-manifolds via closed $n$-manifolds?

Published on 11 Apr 2026 - 11:14

List Question

Show that the index of $r$ must be the sum of the indices of $p$ and $q$.

submanifold and open subset

How can I show that $a,b \in Z$?

The solution set in $\mathbb{R}^3 - \{0\}$ of $x^d +y^d= z^d$ has the form $p^{-1}(X_d)$.

Non degenerate critical points.

What is $g$ in Guillemin and Pollack's Differential Topology?

$f: X \to Y$ is a submersion, $X$ is compact and $Y$ is connected - why $f(X)$ is open?

Projection, canonical immersion/submersion - are they equivalent, and are they open maps?

How to draw the conclusion that $f$ is continuous?

The independence of gradient.

GP 1.4.4 An extension of partial converse of preimage theorem.

$\mathbb{R}^k$ and $\mathbb{R}^k$ are trivially diffeomorphic.

Finite approximation of path space.

If $p$ is homogeneous of order $k$, then $p^{-1}(a)$ is diffeomorphic to $p^{-1}(b)$

studying compact $\partial$-$n$-manifolds via closed $n$-manifolds?

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