User R_D

11 votes

0 answers

267 views

How to prove this is a fibre bundle?

asked Jun 27, 2015 at 6:32

10 votes

4 answers

2k views

Is this dual pairing the same as the inner product?

linear-algebra vector-spaces inner-products

asked Jun 9, 2015 at 13:46

10 votes

1 answer

432 views

Equivalence of two definitions of Spin structure

algebraic-topology differential-topology vector-bundles

asked Sep 26, 2016 at 7:17

9 votes

0 answers

137 views

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

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

asked Apr 15, 2016 at 9:19

9 votes

1 answer

2k views

Is the action of a finite group always discontinuous?

general-topology topological-groups group-actions

asked Oct 24, 2015 at 11:54

9 votes

2 answers

2k views

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

algebraic-topology

asked Feb 24, 2016 at 12:00

8 votes

1 answer

193 views

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

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

asked Nov 15, 2016 at 6:09

7 votes

0 answers

231 views

Proving that the given map has the path lifting property

algebraic-topology group-actions

asked Oct 21, 2015 at 4:46

7 votes

1 answer

263 views

Is Homeo$(X)$ metrizable?

general-topology metric-spaces

asked Oct 3, 2015 at 13:25

7 votes

1 answer

524 views

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

algebraic-topology covering-spaces quotient-spaces

asked Jan 28, 2015 at 16:24

6 votes

3 answers

411 views

Definition of a Manifold from Guillemin Pollack

multivariable-calculus differential-geometry differential-topology

asked Nov 23, 2014 at 16:27

6 votes

1 answer

537 views

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

algebraic-geometry sheaf-theory schemes

asked Nov 19, 2015 at 13:21

6 votes

1 answer

240 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

asked Nov 30, 2015 at 15:51

5 votes

2 answers

1k views

$f:X\rightarrow Y$ is a closed immersion iff $f:f^{-1}(U_i)\rightarrow U_i$ is a closed immersion.

algebraic-geometry schemes

asked Dec 11, 2015 at 8:13

5 votes

0 answers

673 views

Definition of geometric vector bundle from Hartshorne

algebraic-geometry vector-bundles

asked Nov 22, 2015 at 11:22

5 votes

1 answer

76 views

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

general-topology algebraic-topology group-actions

asked Oct 23, 2015 at 6:17

5 votes

1 answer

78 views

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

algebraic-topology lie-groups

asked Nov 12, 2015 at 6:51

5 votes

1 answer

305 views

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

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

asked Feb 22, 2016 at 13:37

5 votes

3 answers

347 views

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

abstract-algebra general-topology group-actions

asked Feb 22, 2016 at 18:15

5 votes

2 answers

321 views

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

abstract-algebra modules

asked May 30, 2015 at 16:26

5 votes

2 answers

136 views

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

general-topology algebraic-topology

asked Oct 25, 2015 at 6:37

5 votes

1 answer

106 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

asked Oct 19, 2015 at 6:31

5 votes

3 answers

463 views

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

abstract-algebra commutative-algebra intuition

asked Dec 8, 2017 at 14:27

5 votes

1 answer

155 views

Is there a way to calculate the sum of absolute values of the roots of a cubic polynomial without actually computing the roots?

algebra-precalculus polynomials roots cubics

asked Apr 25, 2020 at 16:24

5 votes

1 answer

390 views

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

algebraic-topology group-actions covering-spaces

asked Feb 26, 2016 at 4:54

5 votes

1 answer

706 views

On the definition of a reductive group.

algebraic-geometry definition algebraic-groups

asked Jun 18, 2016 at 12:29

5 votes

2 answers

558 views

How to write the commutator subgroup in terms of the generators of the group?

abstract-algebra group-theory group-presentation

asked Jul 9, 2016 at 12:11

4 votes

4 answers

545 views

Proving a symmetric Cauchy matrix is positive semidefinite

linear-algebra matrices positive-semidefinite cauchy-matrices

asked Jan 17, 2020 at 15:18

4 votes

3 answers

208 views

Perron Frobenius theorem for matrices with entries from $\{-1,0,1\}$

linear-algebra matrices reference-request eigenvalues-eigenvectors

asked Jun 6, 2021 at 8:16

4 votes

2 answers

150 views

If $A$ and $B$ have non-negative eigen values then can we conclude that $A+B$ has non-negative eigen values?

linear-algebra matrices eigenvalues-eigenvectors

asked Mar 30, 2020 at 7:17

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153 Questions

How to prove this is a fibre bundle?

Is this dual pairing the same as the inner product?

Equivalence of two definitions of Spin structure

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

Is the action of a finite group always discontinuous?

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

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

Proving that the given map has the path lifting property

Is Homeo$(X)$ metrizable?

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

Definition of a Manifold from Guillemin Pollack

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

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

$f:X\rightarrow Y$ is a closed immersion iff $f:f^{-1}(U_i)\rightarrow U_i$ is a closed immersion.

Definition of geometric vector bundle from Hartshorne

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

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

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?

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

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

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

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

Is there a way to calculate the sum of absolute values of the roots of a cubic polynomial without actually computing the roots?

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

On the definition of a reductive group.

How to write the commutator subgroup in terms of the generators of the group?

Proving a symmetric Cauchy matrix is positive semidefinite

Perron Frobenius theorem for matrices with entries from $\{-1,0,1\}$

If $A$ and $B$ have non-negative eigen values then can we conclude that $A+B$ has non-negative eigen values?