User R_D

1

11

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0

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202

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How to prove this is a fibre bundle?

Jul 2 '15 at 5:39 Community♦ 1

2

8

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2

answers

1k

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Is the action of a finite group always discontinuous?

general-topology topological-groups group-actions

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5

8

votes

1

answer

141

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Is there a name given to a space whose first three Stiefel-Whitney classes vanish?

algebraic-topology manifolds differential-topology characteristic-classes obstruction-theory

Dec 30 '16 at 12:30 Michael Albanese 72.8k

2

8

votes

1

answer

264

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Equivalence of two definitions of Spin structure

algebraic-topology differential-topology vector-bundles

Oct 3 '16 at 15:30 Community♦ 1

3

8

votes

0

answers

119

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algebraic-topology lie-groups group-actions covering-spaces

Aug 10 '16 at 4:37 Community♦ 1

2

8

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3

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linear-algebra vector-spaces inner-product-space

Jun 9 '15 at 15:22 Zavosh 5,446

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7

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180

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Is Homeo$(X)$ metrizable?

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1

7

votes

2

answers

1k

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Universal cover of $\mathbb R^2\setminus\{0\}$

algebraic-topology

Feb 24 '16 at 17:14 Community♦ 1

7

votes

0

answers

164

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Proving that the given map has the path lifting property

algebraic-topology group-actions

Oct 22 '15 at 4:31 R_D 5,924

1

6

votes

1

answer

108

views

$\phi:\mathcal F\rightarrow \mathcal G$ is an isomorphism if there is an open cover on which $\phi(U)$ is an isomorphism.

algebraic-geometry sheaf-theory

Nov 30 '15 at 16:17 Jakob Oesinghaus 614

3

6

votes

1

answer

375

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Why is the rank of a locally free sheaf same everywhere if $X$ is connected?

algebraic-geometry sheaf-theory schemes

Nov 19 '15 at 18:34 MooS 27.7k

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6

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1

answer

361

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If the fibers of a quotient map are all discrete, is this map a covering map?

algebraic-topology covering-spaces quotient-spaces

Jan 28 '15 at 16:43 Najib Idrissi 45.5k

5

votes

1

answer

228

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Is the quotient $X/G$ homeomorphic to $\tilde{X}/G'$?

algebraic-topology group-actions covering-spaces

Feb 26 '16 at 23:44 Community♦ 1

1

5

votes

1

answer

177

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On lifting an action of $G$ on $X$ to an action of $G'$ on $\tilde{X}$.

general-topology algebraic-topology lie-groups group-actions

Feb 22 '16 at 21:10 Lee Mosher 64.9k

5

votes

3

answers

175

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Is the action of $\mathbb Z$ on $\mathbb R$ by translation the only such action?

abstract-algebra general-topology group-actions

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5

votes

1

answer

71

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algebraic-topology lie-groups

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1

5

votes

2

answers

107

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general-topology algebraic-topology

Oct 25 '15 at 6:54 Eric Wofsey 227k

5

votes

1

answer

65

views

What is the closure of $S^1\times \mathbb{Z}$ in Homeo$(S^2\times \mathbb{R})$?

general-topology algebraic-topology group-actions

Oct 23 '15 at 21:34 V. Rogov 899

1

5

votes

1

answer

90

views

If $G$ is a group of isometries of $X$ then prove that $X/G$ and $X/\bar{G}$ are homotopically equvalent

general-topology algebraic-topology metric-spaces homotopy-theory group-actions

Oct 23 '15 at 13:30 R_D 5,924

1

5

votes

2

answers

215

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What are the direct summands in $\mathbb{Z}^n$?

abstract-algebra modules

May 31 '15 at 7:58 user26857 40.6k

1

5

votes

3

answers

281

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Definition of a Manifold from Guillemin Pollack

multivariable-calculus differential-geometry differential-topology

Apr 5 '15 at 7:15 zenos 35

1

4

votes

3

answers

224

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What is the intuition behind saying that the nilradical is the intersection of prime ideals?

abstract-algebra commutative-algebra intuition

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4

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2

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166

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Does $\pi_1(X, x_0)$ act on $\tilde{X}$?

algebraic-topology group-actions covering-spaces

Feb 25 '16 at 11:45 John Hughes 73.1k

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4

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97

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The closure of $\mathbb{Z\times Z\times R}$ in Homeo$(\mathbb R^2)$ is the group of translations of $\mathbb R^2$

general-topology algebraic-topology group-actions

Dec 22 '15 at 20:31 Community♦ 1

2

4

votes

0

answers

390

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Definition of geometric vector bundle from Hartshorne

algebraic-geometry vector-bundles

Nov 22 '15 at 11:22 R_D 5,924

1

4

votes

0

answers

126

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Is $D$ a metric on $X/G$ and does it induce the quotient topology?

general-topology metric-spaces group-actions quotient-spaces

Nov 1 '15 at 13:54 R_D 5,924

4

votes

0

answers

60

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group-theory group-homomorphism continuous-homomorphisms

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2

3

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4

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131

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Proving a symmetric Cauchy matrix is positive semidefinite

linear-algebra matrices positive-semidefinite cauchy-matrices

Jan 19 at 20:41 Rodrigo de Azevedo 14.5k

1

3

votes

3

answers

73

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Uniform convergence of the series $\sum(nx)^{-2}$

real-analysis sequences-and-series

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2

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480

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linear-algebra abstract-algebra modules matrix-decomposition smith-normal-form

Apr 18 '18 at 17:41 Rodrigo de Azevedo 14.5k

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138 Questions

How to prove this is a fibre bundle?

Is the action of a finite group always discontinuous?

Is there a name given to a space whose first three Stiefel-Whitney classes vanish?

Equivalence of two definitions of Spin structure

Is this covering group $G'$ of $G$ unique?

Is this dual pairing the same as the inner product?

Is Homeo$(X)$ metrizable?

Universal cover of $\mathbb R^2\setminus\{0\}$

Proving that the given map has the path lifting property

$\phi:\mathcal F\rightarrow \mathcal G$ is an isomorphism if there is an open cover on which $\phi(U)$ is an isomorphism.

Why is the rank of a locally free sheaf same everywhere if $X$ is connected?

If the fibers of a quotient map are all discrete, is this map a covering map?

Is the quotient $X/G$ homeomorphic to $\tilde{X}/G'$?

On lifting an action of $G$ on $X$ to an action of $G'$ on $\tilde{X}$.

Is the action of $\mathbb Z$ on $\mathbb R$ by translation the only such action?

Where have we used that $G$ is a compact Lie group?

If $f:X\rightarrow Y$ has the path lifting property the so does $f|_A$?

What is the closure of $S^1\times \mathbb{Z}$ in Homeo$(S^2\times \mathbb{R})$?

If $G$ is a group of isometries of $X$ then prove that $X/G$ and $X/\bar{G}$ are homotopically equvalent

What are the direct summands in $\mathbb{Z}^n$?

Definition of a Manifold from Guillemin Pollack

What is the intuition behind saying that the nilradical is the intersection of prime ideals?

Does $\pi_1(X, x_0)$ act on $\tilde{X}$?

The closure of $\mathbb{Z\times Z\times R}$ in Homeo$(\mathbb R^2)$ is the group of translations of $\mathbb R^2$

Definition of geometric vector bundle from Hartshorne

Is $D$ a metric on $X/G$ and does it induce the quotient topology?

What is $\operatorname{Hom}((S^1)^k , (S^1)^n)$?

Proving a symmetric Cauchy matrix is positive semidefinite

Uniform convergence of the series $\sum(nx)^{-2}$

Reducing a matrix to Smith normal form