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visits member for 4 years, 2 months
seen Sep 15 at 17:52

Graduate student in mathematics.


Apr
8
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
@user7887: i'm still confused, at the $k$th step we do not know if the group is $Z_2 \oplus Z_{2^{k-1}}$ or $Z_{2^k}$. Showing that there is an element $x$ such that $2x$ is not trivial does not distinguish these in general (only for the $RP^4$ case).
Apr
7
comment Suppose that $x > 1$. Prove that $s_n \to 1$
Showing 1 is a lower bound then means 0 can't be the limit. But just showing that 0 is a lower bound does not rule out 0 as the limit (so your proof is not complete).
Apr
7
comment Suppose that $x > 1$. Prove that $s_n \to 1$
I don't see how you can conclude that the limit must be 1. You know its decreasing and that the limit is either 0 or 1. It starts above 1 so why can't it decrease all the way to 0? However, it's not too hard to show that 1 is a lower bound as well.
Apr
7
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
@user7887: I spent some time on it but was not able to get anywhere. I was also unable to find what you referenced in my edition of Atiyah.
Apr
6
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
I don't understand the Stiefel-Whitney class argument. First of all $w(RP^n)$ vanishes if $n+1$ is a power of two. Secondly we are considering complex vector bundles and it is possible for the complexification of a non-trivial real vector bundle to be trivial (e.g. the complexification of the mobius bundle).
Apr
2
comment $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
Thanks for the answer. I'm not familiar with the Veronese embedding. I found this en.wikipedia.org/wiki/Veronese_surface#Veronese_map but I don't think this is what you're talking about since this map doesn't always give a map $P^n \to P^{2n+1}$. Also, how do you see from the spectral sequence that the map is surjective?
Apr
1
awarded  Nice Question
Mar
30
revised Is correct to say that every tensor is a spinor but not every spinor is a tensor?
edited body
Mar
30
answered Is correct to say that every tensor is a spinor but not every spinor is a tensor?
Mar
30
answered Exercise about smooth maps in Lee
Mar
30
comment Exercise about smooth maps in Lee
But you're working locally so take your coordinate neighborhood. Then take say the compact ball. Then you have a bump function which is identically 1 on the compact ball. But now look at the interior of the ball which is also homeomorphic to $\mathbb R^n$ and so gives you another chart in your atlas. So you can always take a chart contained in a compact set and then extend any function on that chart using a bump function.
Mar
30
comment Exercise about smooth maps in Lee
By using a bump function, you can extend any smooth function defined on only a subset to a global smooth function. I think this may help.
Mar
30
comment Exercise about smooth maps in Lee
I'm confused, $C^\infty(F^{-1}(V))$ are functions on a subset of $M$, so you can't pull these back via $F$. Maybe you want to show $C^\infty(F^{-1}(V)) \subset F^* C^\infty(V)$?
Mar
30
revised $K(\mathbb R P^n)$ from $K(\mathbb C P^k)$
added 956 characters in body
Mar
29
comment Unknown method (for me) to obtain the value of a variable
This is the "Fourier trick."
Mar
28
answered Lie algebra of a quotient of Lie groups
Mar
27
revised Why is the orthogonal group $\operatorname{O}(2n,\mathbb R)$ not the direct product of $\operatorname{SO}(2n, \mathbb R)$ and $\mathbb Z_2$?
added 98 characters in body
Mar
27
answered Why is the orthogonal group $\operatorname{O}(2n,\mathbb R)$ not the direct product of $\operatorname{SO}(2n, \mathbb R)$ and $\mathbb Z_2$?
Mar
26
comment mathematical existence
"to be is to be the value of a variable"
Mar
25
awarded  Taxonomist