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Graduate student in mathematics.


Mar
23
comment Which is the “proper” definition of a geodesic curve?
I don't think there can ever be a longest path: if $\gamma$ is a path then we can compose $\gamma$ with the path taking us backwards along $\gamma$ and then compose again with $\gamma$ to get a path 3 times as long as $\gamma$. Edit: I'm guessing though you meant local maximum.
Mar
15
answered Quotient map in polynomial ring
Mar
14
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
@user7887 $\mathbb R P^n$ is a quotient of $S^n$, not a subspace. The long exact sequence is for a pair $(X,Y)$ where $Y \subset X$.
Mar
13
comment vector space of all smooth functions has infinite dimension
You can use this fact to prove the desired result. Define a polynomial locally in a chart and extend it to the entire manifold by multiplying with a bump function. Then you'll get an infinite dimensional subspace of $C^\infty$ in this way.
Mar
13
comment Motivation for product structure
I don't see why integrability should be necessary. I would guess that $E$ is integrable if (only if?) $J$ is since if $J$ is integrable we get our $z_i$ and $\bar z_i$ coordinates from which we can define $E$. I don't know why it would induce a $G$-structure.
Mar
13
answered Motivation for product structure
Mar
13
comment Motivation for product structure
Or do you mean Lie group structure?
Mar
13
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
$\mathbb RP^n$ is not a subspace of $S^n$ so I don't see how you can consider the pair $(S^n, \mathbb RP^n)$.
Mar
12
comment Asking an exact sequence of $K(X)$ modules
That's the version of the book I have but I couldn't find what you quoted. What section is it in?
Mar
12
answered Why abstract manifolds?
Mar
12
comment For all integers b, c, and d, if x is rational such that x^2+bx+c=d, then x is an integer
$x^2 + 2x + 3 = 4$ does not provide a counterexample since the solutions to that equation are not rational anyways.
Mar
12
comment For all integers b, c, and d, if x is rational such that x^2+bx+c=d, then x is an integer
Be careful: x = 1/2 * (some number) does not mean that x is not an integer since (some number) could be a multiple of 2.
Mar
11
comment Asking an exact sequence of $K(X)$ modules
what edition of the book do you have...it's not on page 76 in my version and I can't find that sequence anywhere.
Mar
11
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
I understand how to get the K group for $\mathbb C P^n$ in that way, but I do not think this will work for $\mathbb R P^n$. The complex case seems to involve crucially the fact that $CP^n$ has cells only in even dimensions so that the sequence breaks up into short exact sequences.
Mar
11
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
How do you compute K groups using cell structures? Is this the same as using the Atiyah-Hirzburch spectral sequence? If so, I think it is difficult to get $K(\mathbb RP^n)$ this way since you get a group extension problem.
Mar
11
asked $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
Mar
9
awarded  Nice Question
Mar
9
comment vector space of continuous functions on compact Hausdorff space
You probably want to clarify what you mean. Your first statement says the vector space is always infinite dimensional but then you ask when is it finite dimensional. In any case, if your space is finite then the vector space is finite dimensional, with the dimension equal to the number of points in your space.
Mar
8
answered Practice problem from Mean Value Theorem in Real Analysis
Mar
8
accepted Does naturality imply isomorphism invariance for characteristic classes?