Reputation
873
Next privilege 1,000 Rep.
Create new tags
Badges
1 7
Newest
 Revival
Impact
~10k people reached

Aug
14
comment Is $\mathbb{S}^1 \wedge E$ a cofinal subspectra in $\Sigma E$?
If $\mathbb S^1\wedge E$ is cofinal in $\Sigma E$, then the two must be isomorphic. As long as the author really does use cofinality, the proof is indeed trivial. I would have to see the argument to check that cofinality is used.
Aug
14
revised Is exterior algebra an example of an algebra over a field?
added 17 characters in body
Aug
14
revised Is exterior algebra an example of an algebra over a field?
added 17 characters in body
Aug
14
answered Is exterior algebra an example of an algebra over a field?
Aug
13
answered How to determine if division by zero causes a derivative to not exist?
Aug
13
comment How to determine if division by zero causes a derivative to not exist?
could you clarify your notation? What v.f. is $\hat{r}$? Is it $\hat{r}(x,y)=\langle x,y\rangle$?
Jul
22
awarded  Revival
Jul
6
comment “Basis extension theorem” for local smooth vector fields
@AndrewD.Hwang Absolutely, in general $U$ may not be contractible and of course the proof would fall apart. I do mean $U\cap V$ for some sufficiently small, contractible open set $V$ containing $p$.
Jun
8
comment What are $E_\infty$-rings?
@AaronMezel-Gee Thanks. I'll check it out.
Jun
8
comment What are $E_\infty$-rings?
@AaronMazel-Gee I'm fairly well acquainted with the operad story. I was a bit more interested in the derived algebraic geometry part.
Jun
7
comment What are $E_\infty$-rings?
@AaronMazel-Gee This is a great summary of a lot of material! Do you have expository notes that expand on this? I know the pieces of the story, but it would be worth while to sit down and "connect all the dots" (as you clearly have).
Feb
24
revised Kernel of a Constant Rank Bundle Map Using the Constant Rank Theorem
deleted 9 characters in body
Feb
24
answered Kernel of a Constant Rank Bundle Map Using the Constant Rank Theorem
Feb
24
comment Kernel of a Constant Rank Bundle Map Using the Constant Rank Theorem
Also, the statement that $F$ has constant rank (as a smooth map between manifolds) means that the derivative $dF$ has constant rank as a map between tangent bundles. Hence, to fit it in to your context, $dF$ would need to have constant rank as a map of the tangent bundles over the TOTAL spaces $E$ and $E^{\prime}$.
Feb
24
comment Kernel of a Constant Rank Bundle Map Using the Constant Rank Theorem
I don't think you'll be able to use this. Since the total spaces of each bundle is a smooth manifold, certainly $F^{-1}(s(p))$ is an embedded submanifold ($s$ is the zero section, $p$ a point on the base). In fact, it's a subspace of the fiber. The problem is stitching these sub manifolds together smoothly.
Feb
24
comment Kernel of a Constant Rank Bundle Map Using the Constant Rank Theorem
What do you mean by the kernel of a smooth map. If you mean it's derivative, then this would be a special case of the claim where $E$ is the tangent bundle.
Feb
9
revised Question on tangent spaces
misspelled question
Feb
9
suggested approved edit on Question on tangent spaces
Feb
8
answered What to answer when people ask what I do in mathematics
Jan
30
comment Algebraic multiplicity of an eigen value
Algebraic multiplicity is just the degree of the linear term corresponding to $\lambda$ in the characteristic polynomial. Every matrix is similar to an upper triangular matrix and the determinant is invariant under similarity. Is this not enough to prove the claim?