Reputation
16,524
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
3 33 73
Newest
 Enlightened
Impact
~345k people reached

2d
comment Surgery to unlink $S^1$ and $S^2$ in $S^4$
What do you mean when you say two disjoint submanifolds of a given manifold are "unlinked"?
Apr
7
comment A question about the index of vector field
Yes, an argument like that works.
Apr
7
comment A question about the index of vector field
What tools are you working with? Homology/cohomology/poincare duality, or are you working with transversality? There are approaches to your question from both directions.
Apr
7
comment A question about the index of vector field
Oh now I see. Your map $v$ is of the form $v : \partial U \to S^k$ and it extends to a map $v : U \to S^k$ is that correct? I assume $k$ is the dimension of $\partial U$.
Apr
7
comment A question about the index of vector field
Your question is ill-formed. It looks like you want to ask about something related to the Poincare-Hopf index theorem, but for manifolds with boundary. But when you refer to the "index" you do not supply any real context. Which index are you talking about?
Apr
1
reviewed Close Cuts and cycles in graph, edges in common
Apr
1
reviewed Close Why didn't Bernoulli and Euler use an integral comparison to estimate the solution to the Basel problem?
Apr
1
reviewed Close Is the functional equation $f(x+y)=f(x)+f(y)$ on $\mathbb{R}_{+}$ solved only by linear functions?
Apr
1
reviewed Close Probability of exactly k out of n events occuring
Apr
1
reviewed Close Negative integers congruent modulo m
Apr
1
reviewed Close Laplace equation in polar coordinates
Apr
1
reviewed Leave Open Parametric representation of a plane cut of a sphere at y=5
Apr
1
comment $SL(3,\mathbb{R})$ is a smooth manifold?
You'll need to compute the derivative of the determinant map.
Mar
31
comment Generalize Gauss-Bonnet Formula to non-simple closed curves
You aren't really talking about an extension of the Gauss-Bonnet Formula, more just one of the standard ways of stating it. Isn't it stated essentially the above way in Milman-Parker, for instance?
Mar
26
comment Poincare-Lefschetz duality, universal coefficients, and middle cohomology
Yes, it's possible to not only compute $r$ but to compute all the maps. Is that all you want to know?
Mar
26
reviewed Close A textbook for a rigorous introduction to Stochastic Analysis with emphasis on stochastic differential equations
Mar
26
reviewed Close Prove that if $x,y,z>0$, then $ \frac {x+y}{x^2+y^2} + \frac {y+z}{y^2+z^2} + \frac {z+x}{z^2+x^2} \leq \frac 1x + \frac 1y + \frac 1z$
Mar
25
comment The Hodge $*$-operator and the wedge product
I put an answer to your question in the MO thread: mathoverflow.net/questions/162366/…
Mar
25
answered First proof of Poincaré Lemma
Mar
23
comment Clarification on notation of “left invariant fields” (Lie groups)
If $G$ is a matrix group, $X(A) = AB$ is left-invariant for any matrix $B$ fixed. Similarly, $Y(A) = BA$ is right-invariant for any $B$ fixed. As Amitsh mentions $d$ is a way of writing the derivative (as a linear transformation).