Question

Faithful group actions for singleton group or for empty set

score 162 · Answer 1 · 2019-10-14 13:32:25

162

Views

Faithful group actions for singleton group or for empty set

Published on 14 Oct 2019 - 13:32

score 314 · Answer 2 · 2019-10-14 14:13:12

314

Views

Some element has trivial stabilizer or isotropy subgroup, i.e. $G$ and orbit $xG$ bijectively correspond. What's the term for this?

Published on 14 Oct 2019 - 14:13

score 213 · Answer 3 · 2019-10-14 14:15:11

213

Views

Whether or not a group action on a possibly empty set is transitive if for all elements in the set, their orbits equal the set

Published on 14 Oct 2019 - 14:15

score 395 · Answer 4 · 2019-10-14 14:33:51

395

Views

In the context of free or faithful group actions, what is the stabilizer subgroup when the set is empty?

Published on 14 Oct 2019 - 14:33

score 152 · Answer 5 · 2019-10-14 15:04:53

152

Views

Free group actions for singleton group or for empty set

Published on 14 Oct 2019 - 15:04

score 443 · Answer 6 · 2019-10-14 15:48:19

443

Views

A group action is regular if and only if free and transitive. I have questions on the non-empty part.

Published on 14 Oct 2019 - 15:48

score 400 · Answer 7 · 2026-03-25 16:02:59

400

Views

Definition of principal $G$-bundle might be missing details or have implicit assumptions on actions on each trivializing open set

Published on 25 Mar 2026 - 16:02

score 85 · Answer 8 · 2019-10-17 11:07:32

85

Views

What does it mean for right equivariant maps to be left translations?

Published on 17 Oct 2019 - 11:07

score 326 · Answer 9 · 2019-10-18 09:03:37

326

Views

Manifold structure such that a bijection of sets becomes a diffeomorphism of manifolds? Group structure for group isomorphism?

Published on 18 Oct 2019 - 9:03

score 79 · Answer 10 · 2019-10-22 11:50:47

79

Views

Why use left multiplication to prove frame manifold is well-defined? Can $(M,\mathscr A)$ and $(M,\mathscr B)$ be diffeo, with identity not a diffeo?

Published on 22 Oct 2019 - 11:50

score 2.7k · Answer 11 · 2019-10-22 18:14:42

2.7k

Views

Orbits of Group Actions

Published on 22 Oct 2019 - 18:14

score 56 · Answer 12 · 2026-03-26 12:37:30

56

Views

Orbits and stabilisers of $D_{8}$ on set of 2-subsets of $\{1,2,3,4\}$

Published on 26 Mar 2026 - 12:37

score 230 · Answer 13 · 2026-03-26 04:13:26

230

Views

How to visualize group elements as actions?

Published on 26 Mar 2026 - 4:13

score 359 · Answer 14 · 2019-10-26 04:48:51

359

Views

Kernel of an action through left multiplication is

Published on 26 Oct 2019 - 4:48

score 36 · Answer 15 · 2019-10-26 06:45:19

36

Views

Prove that $X_p$ is a vector at $p$

Published on 26 Oct 2019 - 6:45

List Question

Faithful group actions for singleton group or for empty set

Some element has trivial stabilizer or isotropy subgroup, i.e. $G$ and orbit $xG$ bijectively correspond. What's the term for this?

Whether or not a group action on a possibly empty set is transitive if for all elements in the set, their orbits equal the set

In the context of free or faithful group actions, what is the stabilizer subgroup when the set is empty?

Free group actions for singleton group or for empty set

A group action is regular if and only if free and transitive. I have questions on the non-empty part.

Definition of principal $G$-bundle might be missing details or have implicit assumptions on actions on each trivializing open set

What does it mean for right equivariant maps to be left translations?

Manifold structure such that a bijection of sets becomes a diffeomorphism of manifolds? Group structure for group isomorphism?

Why use left multiplication to prove frame manifold is well-defined? Can $(M,\mathscr A)$ and $(M,\mathscr B)$ be diffeo, with identity not a diffeo?

Orbits of Group Actions

Orbits and stabilisers of $D_{8}$ on set of 2-subsets of $\{1,2,3,4\}$

How to visualize group elements as actions?

Kernel of an action through left multiplication is

Prove that $X_p$ is a vector at $p$

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