Ryan Budney
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 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"? Apr7 comment A question about the index of vector field Yes, an argument like that works. Apr7 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. Apr7 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 $\partial U$. Apr7 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? Apr1 reviewed Close Cuts and cycles in graph, edges in common Apr1 reviewed Close Why didn't Bernoulli and Euler use an integral comparison to estimate the solution to the Basel problem? Apr1 reviewed Close Is the functional equation $f(x+y)=f(x)+f(y)$ on $\mathbb{R}_{+}$ solved only by linear functions? Apr1 reviewed Close Probability of exactly k out of n events occuring Apr1 reviewed Close Negative integers congruent modulo m Apr1 reviewed Close Laplace equation in polar coordinates Apr1 reviewed Leave Open Parametric representation of a plane cut of a sphere at y=5 Apr1 comment $SL(3,\mathbb{R})$ is a smooth manifold? You'll need to compute the derivative of the determinant map. Mar31 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? Mar26 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? Mar26 reviewed Close A textbook for a rigorous introduction to Stochastic Analysis with emphasis on stochastic differential equations Mar26 reviewed Close Prove that if $x,y,z>0$, then $\frac {x+y}{x^2+y^2} + \frac {y+z}{y^2+z^2} + \frac {z+x}{z^2+x^2} \leq \frac 1x + \frac 1y + \frac 1z$ Mar25 comment The Hodge $*$-operator and the wedge product I put an answer to your question in the MO thread: mathoverflow.net/questions/162366/… Mar25 answered First proof of Poincaré Lemma Mar23 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).