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Aug 28, 2019 at 23:34 vote accept Ali Taghavi
Aug 24, 2019 at 15:57 history edited Francois Ziegler CC BY-SA 4.0
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Aug 24, 2019 at 10:50 history became hot network question
Aug 24, 2019 at 8:12 answer added abx timeline score: 7
Aug 24, 2019 at 3:17 vote accept Ali Taghavi
Aug 24, 2019 at 4:49
Aug 24, 2019 at 3:15 comment added Ali Taghavi @LSpice I guess fixed point free maps in odd dimension is constructed linearly with a combination of 90 degree rotation and complex conjugation. But for quaternioun all projective space have FPP (both odd and even). This is proved in Hatcher book.
Aug 24, 2019 at 3:15 review Close votes
Aug 28, 2019 at 3:05
Aug 24, 2019 at 3:13 answer added LSpice timeline score: 4
Aug 24, 2019 at 3:07 comment added Ali Taghavi @LSpice the only complex projective space with fixed point property are $\mathbb{C}P^{2k}$. Please read the revise history of this question. I had changed $\mathbb{C}P^2$ to CP^3, based on the same reason you mentioned.
Aug 24, 2019 at 2:59 comment added LSpice Note that giving a map $f$ as in the question is equivalent to giving a self-map of $P^3\mathbb C$ without fixed points. (I don't know off the top of my head if such a thing exists, but I'll bet someone does.)
Aug 24, 2019 at 2:58 history edited LSpice CC BY-SA 4.0
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Aug 24, 2019 at 2:08 history edited Ali Taghavi CC BY-SA 4.0
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Aug 24, 2019 at 2:05 comment added Ali Taghavi @LSpice yes thanks I revise it.
Aug 24, 2019 at 1:19 comment added LSpice Shouldn't both '$\in$' be '$\subseteq$'?
Aug 24, 2019 at 1:15 history edited Ali Taghavi CC BY-SA 4.0
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Aug 24, 2019 at 0:58 history asked Ali Taghavi CC BY-SA 4.0