Question

Small perturbations of a loop in $\mathbb C$ does not change its winding number

score 103 · Answer 1 · 2021-12-29 02:11:05

103

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Small perturbations of a loop in $\mathbb C$ does not change its winding number

Published on 29 Dec 2021 - 2:11

score 38 · Answer 2 · 2021-12-30 13:43:25

38

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If $ |\phi_1| <| \phi_2| $ and $\phi = \phi_1 + \phi_2 $ then $\mathrm {Ind} _{\phi} (0) = \mathrm {Ind} _{\phi_2} (0)$

Published on 30 Dec 2021 - 13:43

score 198 · Answer 3 · 2022-01-08 16:55:49

198

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How do I show that the winding number of this closed continuous path is zero?

Published on 08 Jan 2022 - 16:55

score 124 · Answer 4 · 2022-01-14 21:15:56

124

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How do I compute the local degree of the following map?

Published on 14 Jan 2022 - 21:15

score 201 · Answer 5 · 2022-03-06 02:29:20

201

Views

"Winding number" of the map $g: T^{2n+1} \to U(N)$

Published on 06 Mar 2022 - 2:29

score 58 · Answer 6 · 2026-03-27 17:52:19

58

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Representations of $\mathfrak{u}(1)$ on $\mathbb{C}$ and $\bar{\mathbb{C}}$ with winding number $k\neq0$ are not isomorphic.

Published on 27 Mar 2026 - 17:52

score 248 · Answer 7 · 2026-03-30 03:36:18

248

Views

Closed rectifiable curve with arbitary winding number.

Published on 30 Mar 2026 - 3:36

score 129 · Answer 8 · 2026-04-11 07:41:43

129

Views

Maps that preserve winding numbers

Published on 11 Apr 2026 - 7:41

score 31 · Answer 9 · 2026-04-10 01:01:47

31

Views

A question about the formula for winding numbers in SMT 2021 Power Round

Published on 10 Apr 2026 - 1:01

score 302 · Answer 10 · 2026-03-28 11:42:12

302

Views

Regarding the winding number

Published on 28 Mar 2026 - 11:42

score 231 · Answer 11 · 2022-05-19 04:54:18

231

Views

How to show that the winding number must be $0$ or $\pm$ $1$ in this case?

Published on 19 May 2022 - 4:54

score 197 · Answer 12 · 2026-04-11 18:35:27

197

Views

Winding number of an ellipse $\gamma$ at $0$ using $\omega(\gamma,0)=\frac{1}{2i\pi}\oint_{\gamma}\frac{1}{z}dz$?

Published on 11 Apr 2026 - 18:35

score 42 · Answer 13 · 2026-04-10 18:21:46

42

Views

Is the winding number of a null-homologous cycle outside an open ball zero?

Published on 10 Apr 2026 - 18:21

score 110 · Answer 14 · 2026-03-27 01:46:49

110

Views

What type of Mathematics, if any, is this? (On curiosities associated with a logo.)

Published on 27 Mar 2026 - 1:46

score 54 · Answer 15 · 2022-08-15 21:21:17

54

Views

Find a closed path so that the number of zeroes is equal to the winding number

Published on 15 Aug 2022 - 21:21

List Question

Small perturbations of a loop in $\mathbb C$ does not change its winding number

If $ |\phi_1| <| \phi_2| $ and $\phi = \phi_1 + \phi_2 $ then $\mathrm {Ind} _{\phi} (0) = \mathrm {Ind} _{\phi_2} (0)$

How do I show that the winding number of this closed continuous path is zero?

How do I compute the local degree of the following map?

"Winding number" of the map $g: T^{2n+1} \to U(N)$

Representations of $\mathfrak{u}(1)$ on $\mathbb{C}$ and $\bar{\mathbb{C}}$ with winding number $k\neq0$ are not isomorphic.

Closed rectifiable curve with arbitary winding number.

Maps that preserve winding numbers

A question about the formula for winding numbers in SMT 2021 Power Round

Regarding the winding number

How to show that the winding number must be $0$ or $\pm$ $1$ in this case?

Winding number of an ellipse $\gamma$ at $0$ using $\omega(\gamma,0)=\frac{1}{2i\pi}\oint_{\gamma}\frac{1}{z}dz$?

Is the winding number of a null-homologous cycle outside an open ball zero?

What type of Mathematics, if any, is this? (On curiosities associated with a logo.)

Find a closed path so that the number of zeroes is equal to the winding number

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