Question

How to show that the integral of this volume-form over $S^n$ isn't 0?

score 78 · Answer 1 · 2021-07-27 19:19:30

78

Views

How to show that the integral of this volume-form over $S^n$ isn't 0?

Published on 27 Jul 2021 - 19:19

score 63 · Answer 2 · 2021-08-03 15:32:41

63

Views

$\mathbf{x}\wedge \mathbf{w} =0$ iff $\mathbf{w}=\mathbf{x}\wedge \mathbf{w}' $

Published on 03 Aug 2021 - 15:32

score 44 · Answer 3 · 2026-03-28 01:07:38

44

Views

Why is it useful to have only $2$ orientations for 3D oriented volumes and not $3!$? (And why not $n!$ for $n$D?)

Published on 28 Mar 2026 - 1:07

score 43 · Answer 4 · 2026-03-30 17:47:51

43

Views

Alternating forms and isometries of the underlying vector space

Published on 30 Mar 2026 - 17:47

score 66 · Answer 5 · 2021-08-06 03:18:07

66

Views

Exercise 3.15 from Introduction to Manifolds by Tu

Published on 06 Aug 2021 - 3:18

score 311 · Answer 6 · 2021-08-10 11:21:57

311

Views

Clarification on notation regarding fields, forms, and exterior algebra

Published on 10 Aug 2021 - 11:21

score 39 · Answer 7 · 2021-08-12 01:08:25

39

Views

Indices of the suspension of a complex

Published on 12 Aug 2021 - 1:08

score 474 · Answer 8 · 2021-08-12 06:42:29

474

Views

Confusion in the order of the differentials in integral using differential forms

Published on 12 Aug 2021 - 6:42

score 1.2k · Answer 9 · 2026-03-26 16:26:43

1.2k

Views

calculating the wedge product for 2 4D vectors

Published on 26 Mar 2026 - 16:26

score 44 · Answer 10 · 2021-09-03 17:54:31

44

Views

how do we show $\wedge^2 I \neq 0$ but $\wedge^2 A=0$?

Published on 03 Sep 2021 - 17:54

score 94 · Answer 11 · 2021-09-05 13:48:31

94

Views

Is this a valid tensor representation of the Hodge star operation?

Published on 05 Sep 2021 - 13:48

score 128 · Answer 12 · 2021-09-06 12:12:09

128

Views

Is the (un-)even part of the exterior algebra an (anti-)commutative sub-algebra?

Published on 06 Sep 2021 - 12:12

score 111 · Answer 13 · 2021-09-07 04:06:26

111

Views

How is the exterior product of multilinear forms defined with exterior algebra

Published on 07 Sep 2021 - 4:06

score 76 · Answer 14 · 2021-09-08 11:47:27

76

Views

$p^{n+1}+p^{n}-p$ = count 2x2 $F_p$-matrices satisfying Grassman algebra relations - true? (And the same for symmetric 3x3 Grassmans)

Published on 08 Sep 2021 - 11:47

score 133 · Answer 15 · 2021-09-12 13:30:51

133

Views

Prove that $\det R = \pm 1$ iff $R \in \mathrm{Isom}(V)$, without using $\det R = \det R^T$

Published on 12 Sep 2021 - 13:30

List Question

How to show that the integral of this volume-form over $S^n$ isn't 0?

$\mathbf{x}\wedge \mathbf{w} =0$ iff $\mathbf{w}=\mathbf{x}\wedge \mathbf{w}' $

Why is it useful to have only $2$ orientations for 3D oriented volumes and not $3!$? (And why not $n!$ for $n$D?)

Alternating forms and isometries of the underlying vector space

Exercise 3.15 from Introduction to Manifolds by Tu

Clarification on notation regarding fields, forms, and exterior algebra

Indices of the suspension of a complex

Confusion in the order of the differentials in integral using differential forms

calculating the wedge product for 2 4D vectors

how do we show $\wedge^2 I \neq 0$ but $\wedge^2 A=0$?

Is this a valid tensor representation of the Hodge star operation?

Is the (un-)even part of the exterior algebra an (anti-)commutative sub-algebra?

How is the exterior product of multilinear forms defined with exterior algebra

$p^{n+1}+p^{n}-p$ = count 2x2 $F_p$-matrices satisfying Grassman algebra relations - true? (And the same for symmetric 3x3 Grassmans)

Prove that $\det R = \pm 1$ iff $R \in \mathrm{Isom}(V)$, without using $\det R = \det R^T$

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