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Jun
11
comment Lie bracket is a connection?
This is the stable webpage: rybu.org/DGNotes If you click on the March 25th, 2015 edition of the notes, it's around page 74, near the start of Chapter 3. Basic properties of connections continue until around page 92.
Jun
9
awarded  Nice Answer
May
10
awarded  Nice Answer
Apr
27
comment Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?
@Zach466920: there's no reason to expect monkeys trapped in a room with typewriters would evolve towards something that would use typewriters for their original purpose. Presumably they would find better things to do with them in the short term.
Apr
24
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 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
25
comment The Hodge $*$-operator and the wedge product
I put an answer to your question in the MO thread: mathoverflow.net/questions/162366/…