User Adam Chalumeau

25 votes

2 answers

1k views

Find $f$ such that $f^{-1}(\lbrace0\rbrace)$ is this knotted curve (M.W.Hirsh)

asked Apr 22, 2019 at 22:41

10 votes

1 answer

415 views

Affine manifolds which are not euclidean manifolds.

differential-geometry manifolds compact-manifolds homogeneous-spaces

asked Jul 12, 2019 at 10:45

9 votes

1 answer

183 views

Is the smallest ball enclosing a compact a Lipschitz function of the compact?

metric-spaces compactness lipschitz-functions

asked Apr 29, 2021 at 12:13

8 votes

2 answers

264 views

What are some examples of incomplete nonextendible manifolds?

differential-geometry riemannian-geometry

asked Dec 7, 2020 at 22:13

7 votes

1 answer

165 views

Local obstruction to having a complete extension

differential-geometry riemannian-geometry geodesic complete-spaces symmetric-spaces

asked Dec 23, 2020 at 21:29

7 votes

1 answer

307 views

Are products of spheres $\prod_i\Bbb S^{n_i}$ different?

general-topology algebraic-topology differential-topology spheres

asked May 26, 2019 at 15:47

6 votes

1 answer

189 views

Is the splitting $\pi_{k}(X,A)\simeq\pi_{k}(X)\times \pi_{k-1}(A)$ a $\pi_1(A)$-modules isomorphism?

algebraic-topology homotopy-theory higher-homotopy-groups

asked Feb 18, 2021 at 16:57

6 votes

2 answers

144 views

Codimension one foliations induced by a map to the circle.

differential-geometry foliations

asked Aug 1, 2019 at 18:03

5 votes

1 answer

435 views

About Poincaré-Hopf theorem: can we find and draw $v$ with only one zero on $S$?

differential-geometry differential-topology surfaces vector-fields

asked Jun 5, 2019 at 18:56

4 votes

1 answer

123 views

Condition for a quotient map to have compact image.

general-topology compactness quotient-spaces

asked Jul 7, 2019 at 10:00

4 votes

1 answer

132 views

$5$-dimensional irreducible representation of $\mathcal{A}_5$

group-theory finite-groups representation-theory characters

asked Feb 28, 2020 at 15:26

3 votes

1 answer

110 views

Submersions from $\Bbb T^2$ to $\Bbb S^1$.

differential-geometry differential-topology fiber-bundles

asked Jul 20, 2019 at 14:12

2 votes

0 answers

36 views

Inhomogeneous complete affine manifolds

differential-geometry manifolds homogeneous-spaces

asked Jul 25, 2019 at 22:04

2 votes

1 answer

95 views

Is the Ricci tensor of a symmetric space proportional to the killing form?

differential-geometry riemannian-geometry lie-algebras symmetric-spaces

asked Mar 1, 2021 at 14:55

2 votes

1 answer

208 views

$\Bbb{S}^1$-bundle over $\Bbb{S}^1$ + reference request

differential-geometry reference-request differential-topology fiber-bundles

asked May 3, 2019 at 21:13

2 votes

1 answer

86 views

Induced morphism on automorphism groups in terms of the original map.

general-topology algebraic-topology covering-spaces

asked May 9, 2019 at 15:06

2 votes

1 answer

77 views

$A=\lambda I_n\iff (\forall M,N\in M_n(\mathbb{R}),~ MN=A \Rightarrow ~ NM=A)$

linear-algebra matrices homothety

asked Apr 20, 2019 at 15:03

1 vote

0 answers

92 views

What are the possible Lie algebras of $K=\rho(\mathbb{R}^2)$, where $\rho :\mathbb{R}^2\to \text{Aff}(\mathbb{R}^2)$?

linear-algebra lie-algebras

asked Apr 18, 2019 at 10:39

1 vote

0 answers

87 views

The projective geometry contains the affine geometry

proof-verification differential-geometry manifolds projective-geometry homogeneous-spaces

asked Jun 3, 2019 at 22:24

1 vote

2 answers

71 views

Definition of Cartan subalgebra in Erdmann-Wildon

lie-algebras semisimple-lie-algebras

asked May 15, 2020 at 8:32

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20 Questions

Find $f$ such that $f^{-1}(\lbrace0\rbrace)$ is this knotted curve (M.W.Hirsh)

Affine manifolds which are not euclidean manifolds.

Is the smallest ball enclosing a compact a Lipschitz function of the compact?

What are some examples of incomplete nonextendible manifolds?

Local obstruction to having a complete extension

Are products of spheres $\prod_i\Bbb S^{n_i}$ different?

Is the splitting $\pi_{k}(X,A)\simeq\pi_{k}(X)\times \pi_{k-1}(A)$ a $\pi_1(A)$-modules isomorphism?

Codimension one foliations induced by a map to the circle.

About Poincaré-Hopf theorem: can we find and draw $v$ with only one zero on $S$?

Condition for a quotient map to have compact image.

$5$-dimensional irreducible representation of $\mathcal{A}_5$

Submersions from $\Bbb T^2$ to $\Bbb S^1$.

Inhomogeneous complete affine manifolds

Is the Ricci tensor of a symmetric space proportional to the killing form?

$\Bbb{S}^1$-bundle over $\Bbb{S}^1$ + reference request

Induced morphism on automorphism groups in terms of the original map.

$A=\lambda I_n\iff (\forall M,N\in M_n(\mathbb{R}),~ MN=A \Rightarrow ~ NM=A)$

What are the possible Lie algebras of $K=\rho(\mathbb{R}^2)$, where $\rho :\mathbb{R}^2\to \text{Aff}(\mathbb{R}^2)$?

The projective geometry contains the affine geometry

Definition of Cartan subalgebra in Erdmann-Wildon