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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 24th 2020

am splitting this off as a stand-alone statement (from complex projective space)

Have cleaned-up the formulation of statement and proof and have generalized from ground ring the complex numbers to reals, complex numbers and quaternions.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 29th 2021

have re-arranged the flow of the proof somewhat. (Previously, half of the proof idea was crammed into the statement of the proposition…)

I really came back here to make a note on the compatibility of cell attachments as we pass from $\mathbb{C}$ to $\mathbb{H}$:

$\array{ S^{4k+3} &\longrightarrow& D^{4(k+1)} \\ \big\downarrow &{}^{{}_{(po)}}& \big\downarrow \\ \mathbb{C}P^{2k+1} &\longrightarrow& \mathbb{C}P^{2k+2} \\ \big\downarrow &{}^{{}_{(po)}}& \big\downarrow \\ \mathbb{H}P^{k} &\longrightarrow& \mathbb{H}P^{k+1} }$

But now I am too tired. Maybe tomorrow…

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 30th 2021

So now I wrote out (here) statement and proof of the above pasting composite.

(This is all elementary and/or trivial. I am just writing it out for peace of mind. Just recently, in another thread, we had a mistake in a similarly “obvious” homotopy-pasting composite, so it’s good to double-check.)