User blancket

9 votes

1 answer

850 views

Galois group of $x^5-x-1$ over $\Bbb Q$

asked Apr 22, 2020 at 6:36

7 votes

2 answers

259 views

$\pi_1(A,x_0)$ acts on the long exact sequence of homotopy groups for $(X,A,x_0)$

algebraic-topology homotopy-theory higher-homotopy-groups

asked Jan 8, 2020 at 16:57

7 votes

1 answer

285 views

Bott Tu Exercise 6.14, integration along the fiber

algebraic-topology differential-topology smooth-manifolds differential-forms vector-bundles

asked Aug 22, 2020 at 8:49

6 votes

1 answer

61 views

Weighted projective plane as a quotient of $\Bbb CP^2$

general-topology algebraic-topology quotient-spaces projective-space

asked Oct 24, 2021 at 3:55

6 votes

1 answer

268 views

Fundamental class of a surface

algebraic-topology homology-cohomology

asked Dec 30, 2019 at 23:17

5 votes

2 answers

85 views

$S^2$ is not a countable union of embedded circles $S^1$

general-topology algebraic-topology homology-cohomology

asked Jan 10, 2020 at 22:59

5 votes

1 answer

138 views

Explicit homotopy on showing that $\pi_n(X,x_0)$ is abelian for $n \geq 2$

algebraic-topology homotopy-theory

asked Jan 6, 2020 at 13:38

5 votes

1 answer

264 views

Theorem 9.13 in Rudin's Real and Complex Analysis

real-analysis measure-theory proof-explanation fourier-transform

asked Mar 8, 2020 at 7:42

5 votes

1 answer

212 views

$\sum_{j=1}^n \frac{\partial}{\partial x_j} (\text{cof}(Df))_{ij}=0$ for a $C^\infty$ function $f:\Bbb R^n\to \Bbb R^n$

real-analysis linear-algebra integration analysis smooth-functions

asked Apr 2, 2020 at 16:16

5 votes

0 answers

75 views

An embedding of $U(n)\to \text{Spin}^c(2n)$

linear-algebra abstract-algebra group-theory clifford-algebras spin-geometry

asked Aug 3, 2021 at 8:21

5 votes

1 answer

157 views

Oriented Grassmann is a $2$-sheeted covering space of Grassmann

algebraic-topology manifolds covering-spaces grassmannian

asked Aug 14, 2020 at 22:40

5 votes

1 answer

152 views

Two definitions of singular cohomology

algebraic-topology homology-cohomology homological-algebra

asked Jun 20, 2020 at 17:01

5 votes

1 answer

102 views

Milnor, Lectures on the h-cobordism theorem, proof of Theorem 3.4

differential-geometry proof-explanation differential-topology smooth-manifolds vector-fields

asked Oct 16, 2020 at 16:47

5 votes

1 answer

80 views

Is it true that $\text{Ext}(A,\Bbb Z)=\text{Ext}(A_{tor},\Bbb Z)$ for any abelian group $A$?

abstract-algebra homological-algebra

asked Apr 8, 2021 at 18:05

4 votes

0 answers

52 views

Intersection number of complex curves in a complex surface

algebraic-geometry complex-geometry intersection-theory

asked Apr 1, 2021 at 12:37

4 votes

1 answer

200 views

Real $2n$-plane bundle with a complex structure is a complex $n$-plane bundle

differential-geometry vector-bundles characteristic-classes almost-complex

asked Jun 19, 2020 at 7:25

4 votes

1 answer

125 views

If $(M,g)$ is a Riemannian manifold and $S$ is a regular level set of $f:M\to \Bbb R$ then $\text{grad}f|_S$ is nowhere vanishing

differential-geometry proof-explanation riemannian-geometry smooth-manifolds orientation

asked Aug 6, 2020 at 16:54

4 votes

1 answer

116 views

Hopf invariant depends only on the homotopy type

algebraic-topology homology-cohomology homotopy-theory cw-complexes

asked Sep 5, 2020 at 20:34

4 votes

2 answers

93 views

Question about the proof of Theorem 3.1 in Morse Theory – Milnor [duplicate]

proof-explanation differential-topology smooth-manifolds morse-theory diffeomorphism

asked Sep 19, 2020 at 11:17

4 votes

1 answer

170 views

Why can the divergence be defined equivalently as ${\rm div}(X)(x)=\sum_j \langle\nabla_j X,e_j\rangle_x$ and $d(i_X dV)=({\rm div}X)dV$?

differential-geometry riemannian-geometry divergence-operator

asked Jul 23, 2021 at 22:52

4 votes

0 answers

120 views

Recovering a covering space via monodromy representation

algebraic-topology homotopy-theory covering-spaces

asked Jun 28, 2021 at 18:26

4 votes

2 answers

93 views

Can $S^k$ be embedded in $S^n$ for all $k>n$?

general-topology algebraic-topology

asked Mar 16, 2020 at 3:09

4 votes

1 answer

186 views

Homotopy type of $\Bbb CP^2 - \Bbb RP^2$

general-topology algebraic-topology homotopy-theory

asked Apr 5, 2020 at 15:02

4 votes

2 answers

67 views

If $G$ is a finite subgroup of $GL_n(C)$ then there is a polynomial $f\in C[x_1,...,x_n]$ such that $f(gv)=f(v)$

linear-algebra abstract-algebra polynomials

asked Apr 5, 2020 at 16:36

4 votes

1 answer

93 views

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

abstract-algebra ring-theory modules homological-algebra noncommutative-algebra

asked Apr 25, 2020 at 23:29

4 votes

2 answers

136 views

Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

real-analysis measure-theory lebesgue-integral lebesgue-measure measurable-functions

asked Apr 27, 2020 at 0:58

4 votes

1 answer

156 views

Postnikov tower of a CW complex is unique up to homotopy equivalence

algebraic-topology homotopy-theory cw-complexes

asked Feb 3, 2020 at 1:57

4 votes

1 answer

314 views

Examples of nicely shrinking sets (Rudin)

measure-theory lebesgue-measure

asked Feb 9, 2020 at 1:59

3 votes

0 answers

91 views

Relative Mapping Cylinders

algebraic-topology homotopy-theory cw-complexes

asked Jan 12, 2020 at 23:59

3 votes

2 answers

140 views

Universal cover of a space with cell attached

algebraic-topology covering-spaces cw-complexes

asked Jan 18, 2020 at 7:53

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268 Questions

Galois group of $x^5-x-1$ over $\Bbb Q$

$\pi_1(A,x_0)$ acts on the long exact sequence of homotopy groups for $(X,A,x_0)$

Bott Tu Exercise 6.14, integration along the fiber

Weighted projective plane as a quotient of $\Bbb CP^2$

Fundamental class of a surface

$S^2$ is not a countable union of embedded circles $S^1$

Explicit homotopy on showing that $\pi_n(X,x_0)$ is abelian for $n \geq 2$

Theorem 9.13 in Rudin's Real and Complex Analysis

$\sum_{j=1}^n \frac{\partial}{\partial x_j} (\text{cof}(Df))_{ij}=0$ for a $C^\infty$ function $f:\Bbb R^n\to \Bbb R^n$

An embedding of $U(n)\to \text{Spin}^c(2n)$

Oriented Grassmann is a $2$-sheeted covering space of Grassmann

Two definitions of singular cohomology

Milnor, Lectures on the h-cobordism theorem, proof of Theorem 3.4

Is it true that $\text{Ext}(A,\Bbb Z)=\text{Ext}(A_{tor},\Bbb Z)$ for any abelian group $A$?

Intersection number of complex curves in a complex surface

Real $2n$-plane bundle with a complex structure is a complex $n$-plane bundle

If $(M,g)$ is a Riemannian manifold and $S$ is a regular level set of $f:M\to \Bbb R$ then $\text{grad}f|_S$ is nowhere vanishing

Hopf invariant depends only on the homotopy type

Question about the proof of Theorem 3.1 in Morse Theory – Milnor [duplicate]

Why can the divergence be defined equivalently as ${\rm div}(X)(x)=\sum_j \langle\nabla_j X,e_j\rangle_x$ and $d(i_X dV)=({\rm div}X)dV$?

Recovering a covering space via monodromy representation

Can $S^k$ be embedded in $S^n$ for all $k>n$?

Homotopy type of $\Bbb CP^2 - \Bbb RP^2$

If $G$ is a finite subgroup of $GL_n(C)$ then there is a polynomial $f\in C[x_1,...,x_n]$ such that $f(gv)=f(v)$

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

Postnikov tower of a CW complex is unique up to homotopy equivalence

Examples of nicely shrinking sets (Rudin)

Relative Mapping Cylinders

Universal cover of a space with cell attached