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Nov
8
asked p divides the index $[G: N_G(P)]$?
Nov
2
awarded  Teacher
Nov
2
answered Find conditions for a polynomial $p$ to be in a vector space $U$
Oct
31
awarded  Editor
Oct
31
revised Seek hint on a problem on Jones' book
add "finite"
Oct
31
suggested approved edit on Seek hint on a problem on Jones' book
Oct
31
comment Seek hint on a problem on Jones' book
I left my first comment because I did not check the reference you gave me, since before I check the reference, my knowledge is that every operator in $B(H)$ is generated by projections, but not necessarily finite, since I only know to use the spectrum theorem to find this linear composition. Now I got it. Thanks again!
Oct
31
accepted Seek hint on a problem on Jones' book
Oct
31
comment Seek hint on a problem on Jones' book
Sorry for my careless reading of your proof and thanks to the answer. I know that I must have be unaware of some points, now I know that I have to use the matrix units in infinite dimensional, thanks for your help!
Oct
31
comment Seek hint on a problem on Jones' book
But the key point is that why can you use $tr(\sum_{i=1}^{\infty}a_i)=\sum_{i=1}^{\infty}tr(a_i)$, to use it, you have assumed that $tr$ is weakly continouous.
Oct
31
comment Seek hint on a problem on Jones' book
for part ii, just use $Tp_k\rightarrow T$, but $tr(Tp_k)=0$, where $p_k$ is the orthognormal projection on the n-dimensional subspace; while for iii, my method only works if we assume $tr(x^*x)>0$ for all nonzero operators.
Oct
31
asked Seek hint on a problem on Jones' book
Oct
26
accepted find the map which induces the homorphism between fundamental groups
Oct
26
comment find the map which induces the homorphism between fundamental groups
Thank you! got it.
Oct
26
comment find the map which induces the homorphism between fundamental groups
Oh, I find that, thank you!
Oct
26
comment find the map which induces the homorphism between fundamental groups
I have not learnt this key lemma, could you give me some reference for this?
Oct
26
asked find the map which induces the homorphism between fundamental groups
Oct
20
comment Can this special amalgamated free product group be trivial group?
@Tara, this is not correct, since $U\cap V\subset U$ does not imply $\pi_1(U\cap V)\rightarrow \pi_1(U)$ is injective. You can check the definition of "Semi-locally simply connected spaces" to see the special case when the image is trivial.
Oct
19
comment Can this special amalgamated free product group be trivial group?
thanks for this nice idea. By the way, I asked this problem because I tried to use Van-kampen's theorem to prove the fundamental group the double of the cone on the Hawaiian Earring (gluing of two mapping cone of the Hawaiian earring along the "bad point") is nontrivial. According to your answer, maybe I need to seek other ways.
Oct
19
accepted Can this special amalgamated free product group be trivial group?