User user302934

9 votes

1 answer

706 views

A covering space in $\Bbb R^3$ exists iff there is an embedding $M_g$ of the 3-torus which induces a surjection

asked Aug 18, 2019 at 19:31

7 votes

0 answers

276 views

Five lemma for homotopy exact sequences of triple

asked May 30, 2021 at 15:36

7 votes

1 answer

152 views

Embeddings of lens spaces in complex projective plane $\Bbb CP^2$

asked Oct 12, 2021 at 6:27

7 votes

0 answers

143 views

Showing that a 4-manifold obtained by attaching a 2-handle is simply-connected

asked Jun 13, 2022 at 4:11

6 votes

3 answers

202 views

Way to determine the type of a knot given by a diagram

asked Jun 8, 2022 at 13:46

6 votes

2 answers

381 views

How to show a space is not a covering space?

asked Aug 18, 2019 at 0:22

6 votes

3 answers

514 views

Bernoulli numbers tend to infinity

asked Nov 26, 2019 at 13:10

5 votes

0 answers

359 views

If a finite group acts on an integral domain which is integrally closed, then the fixed point subring is also integrally closed

asked May 1, 2020 at 7:50

5 votes

1 answer

238 views

Finding subgroups of $G=\langle x,y,z~|~x^2y^2z^2 \rangle$ using covering space theory

asked May 14, 2020 at 11:54

5 votes

1 answer

640 views

Question in Hatcher's Algebraic Topology Exercise 0.27

asked Aug 10, 2019 at 16:47

5 votes

2 answers

276 views

Fundamental group of the space $\Bbb CP^n-p(X)$

asked Sep 22, 2019 at 15:55

5 votes

2 answers

289 views

Degree of a map $T^2\to T^2$ induced by an $2\times 2$ integer matrix

asked Oct 27, 2020 at 1:28

5 votes

1 answer

330 views

The category of finite dimensional right $KG$-modules is equivalent to the category of finite dimensional representations of a quiver $Q$

asked Jun 12, 2020 at 7:47

5 votes

1 answer

84 views

$f\in L^2[0,1]$ iff $f\in L^1[0,1]$ and there is nondecreasing $g$ with $|\int_a^b f(x)dx|^2 \leq (g(b)-g(a))(b-a)$ for $0\leq a\leq b\leq 1$

asked Jul 8, 2020 at 19:39

5 votes

2 answers

403 views

For a complex number $\alpha $ which is algebraic over $\Bbb Q$, determining whether $\bar{\alpha}\in \Bbb Q(\alpha)$ or not

asked Jul 17, 2020 at 1:35

5 votes

1 answer

523 views

Does the action of the fundamental group of a space $X$ on the universal cover $\tilde{X}$ depend on the basepoints?

asked Oct 16, 2021 at 8:07

4 votes

1 answer

190 views

If $(3p_n\pm \sqrt{5p_n^2-4})\Delta/(2p_n)$ is an integer then $p_n$ is an odd-indexed Fibonacci number

asked Dec 15, 2021 at 8:25

4 votes

1 answer

290 views

Codimension inequality of prime ideal in a regular local ring

asked Apr 15, 2022 at 10:15

4 votes

0 answers

138 views

Explicit formula of $S^1$-bundle over $S^2$ with euler number $n$

asked Apr 26, 2022 at 3:05

4 votes

1 answer

158 views

Is $G*G \cong G$ where $G$ is the fundamental group of the Hawaiian earring?

asked Nov 7, 2022 at 4:00

4 votes

1 answer

286 views

A noncomplete inner product space may have a nonempty closed convex subset which does not have a unique element of minimal norm

asked Jun 14, 2020 at 13:44

4 votes

1 answer

173 views

Sign of $df_x$ is locally constant

asked May 13, 2020 at 10:36

4 votes

2 answers

62 views

If unit quaternions $q_1,q_2$ satisfy $q_1^2=q_2^2=-1$, then the map $S^3\to S^3$, $x\mapsto q_1xq_2^{-1}$ has a fixed point

asked Mar 5, 2021 at 12:54

4 votes

1 answer

181 views

Computing the first Chern class of the product of two compact Riemann surfaces

asked Mar 31, 2021 at 12:34

4 votes

2 answers

241 views

The fundamental group of the space $Y=S^3-(p^{-1}(\alpha_1)\cup ... \cup p^{-1}(\alpha_n))$, where $p :S^3 \to \Bbb CP^1$ is the quotient map

asked Sep 21, 2019 at 10:40

4 votes

1 answer

440 views

Homeomorphism lifting a covering map

asked Sep 9, 2019 at 16:05

3 votes

1 answer

431 views

The total ring of fractions of $\Bbb Z_n$

asked Sep 13, 2019 at 13:38

3 votes

3 answers

87 views

Does exactness of $0 \to \Bbb Z^n \to G \to \Bbb Z^m \to 0$ imply $G$ is isomorphic to $\Bbb Z^{m+n}$?

asked Sep 13, 2019 at 17:40

3 votes

1 answer

108 views

Two different maps of a cylinder into $\Bbb R^3$

asked Sep 8, 2019 at 13:01

3 votes

1 answer

453 views

Errata in Hatcher's Algebraic Topology Exercise 1.3.28?

asked Aug 25, 2019 at 8:14

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201 Questions

A covering space in $\Bbb R^3$ exists iff there is an embedding $M_g$ of the 3-torus which induces a surjection

Five lemma for homotopy exact sequences of triple

Embeddings of lens spaces in complex projective plane $\Bbb CP^2$

Showing that a 4-manifold obtained by attaching a 2-handle is simply-connected

Way to determine the type of a knot given by a diagram

How to show a space is not a covering space?

Bernoulli numbers tend to infinity

If a finite group acts on an integral domain which is integrally closed, then the fixed point subring is also integrally closed

Finding subgroups of $G=\langle x,y,z~|~x^2y^2z^2 \rangle$ using covering space theory

Question in Hatcher's Algebraic Topology Exercise 0.27

Fundamental group of the space $\Bbb CP^n-p(X)$

Degree of a map $T^2\to T^2$ induced by an $2\times 2$ integer matrix

The category of finite dimensional right $KG$-modules is equivalent to the category of finite dimensional representations of a quiver $Q$

$f\in L^2[0,1]$ iff $f\in L^1[0,1]$ and there is nondecreasing $g$ with $|\int_a^b f(x)dx|^2 \leq (g(b)-g(a))(b-a)$ for $0\leq a\leq b\leq 1$

For a complex number $\alpha $ which is algebraic over $\Bbb Q$, determining whether $\bar{\alpha}\in \Bbb Q(\alpha)$ or not

Does the action of the fundamental group of a space $X$ on the universal cover $\tilde{X}$ depend on the basepoints?

If $(3p_n\pm \sqrt{5p_n^2-4})\Delta/(2p_n)$ is an integer then $p_n$ is an odd-indexed Fibonacci number

Codimension inequality of prime ideal in a regular local ring

Explicit formula of $S^1$-bundle over $S^2$ with euler number $n$

Is $G*G \cong G$ where $G$ is the fundamental group of the Hawaiian earring?

A noncomplete inner product space may have a nonempty closed convex subset which does not have a unique element of minimal norm

Sign of $df_x$ is locally constant

If unit quaternions $q_1,q_2$ satisfy $q_1^2=q_2^2=-1$, then the map $S^3\to S^3$, $x\mapsto q_1xq_2^{-1}$ has a fixed point

Computing the first Chern class of the product of two compact Riemann surfaces

The fundamental group of the space $Y=S^3-(p^{-1}(\alpha_1)\cup ... \cup p^{-1}(\alpha_n))$, where $p :S^3 \to \Bbb CP^1$ is the quotient map

Homeomorphism lifting a covering map

The total ring of fractions of $\Bbb Z_n$

Does exactness of $0 \to \Bbb Z^n \to G \to \Bbb Z^m \to 0$ imply $G$ is isomorphic to $\Bbb Z^{m+n}$?

Two different maps of a cylinder into $\Bbb R^3$

Errata in Hatcher's Algebraic Topology Exercise 1.3.28?