Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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.
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…
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.)
1 to 3 of 3