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user20353
  • Member for 12 years, 3 months
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22 votes
2 answers
3k views

Grad school & success in the long run

17 votes
1 answer
10k views

The Dimension of the Symmetric $k$-tensors

15 votes
2 answers
2k views

Each point of $M$ has a smooth coordinate neighborhood in which the coordinate frame is orthonormal iff $g$ is flat

15 votes
1 answer
6k views

Learning Homology and Cohomology

14 votes
1 answer
4k views

Covectors $\omega^1, ..., \omega^k$ are linearly dependent iff their wedge product is zero

12 votes
2 answers
11k views

Irreducible in $\mathbb{Z}[\sqrt{-5}]$

10 votes
3 answers
4k views

$\Omega=x\;dy \wedge dz+y\;dz\wedge dx+z\;dx \wedge dy$ is never zero when restricted to $\mathbb{S^2}$

7 votes
3 answers
2k views

Ring theory exercises at the graduate level

7 votes
3 answers
1k views

Unique symmetric covariant $k$-tensor satisfying $(\operatorname{Sym} T)(A,...,A)=T(A,...,A)$ for all $A \in V$

6 votes
2 answers
2k views

$e_1\otimes e_2 \otimes e_3$ cannot be written as a sum of an alternating tensor and a symmetric tensor

5 votes
2 answers
2k views

Real line bundle smoothly isomorphic to Möbius bundle

5 votes
2 answers
652 views

Basis for the set of all covariant $k$-tensors on V

5 votes
1 answer
316 views

Riemannian metric

4 votes
1 answer
249 views

Computing $d\omega$ and $g^\ast \omega$ when $(x,y)=g(s,t)=(st,e^t)$ and $\omega= xdy$

4 votes
1 answer
313 views

Symmetric $k$-tensor

3 votes
1 answer
420 views

Left ideal generated by $\lbrace ab-ba:a,b \in R \rbrace$ is a two-sided ideal

2 votes
1 answer
370 views

Symplectic basis $(A_i,B_i)$ such that $S= $ span$(A_1,B_1,...,A_k,B_k)$ for some $k$ when $S$ is symplectic

2 votes
1 answer
356 views

Symplectic basis $(A_i,B_i)$ such that $S= $ span$(A_1,...,A_k)$ for some $k$ when $S$ is isotropic

2 votes
1 answer
441 views

Dedekind domains

2 votes
2 answers
1k views

The pullback $F^\ast :T^*N \rightarrow T^*M$ is a smooth bundle map

2 votes
3 answers
99 views

$a.b$ is path homotopic to $c.d$