Timeline for Induced maps on homotopy groups by self maps of $\mathbb{CP}^n$

11 events

when toggle format	what		by	license	comment
Sep 4, 2018 at 11:19	vote	accept	Sigur
Aug 12, 2018 at 13:14	comment	added	Sigur		@Dmitri, thanks. We are converging to a complete solution.
Aug 11, 2018 at 23:36	comment	added	mme		Something I missed on a first pass: maps on $\Bbb{CP}^n$ are determined by what they do to a second homology class, not the degree (which is $d^n$). However it is clear that your map is the degree $d$ map on $\Bbb{CP}^1$, so indeed corresponds to $d$.
Aug 11, 2018 at 20:55	comment	added	Dmitri Panov		Yes, Sigur, you are right, thanks for this correction. I have corrected the formula so that the image of the unit $S^{2n+1}$ lies in the unit $S^{2n+1}$. Now one has to explain how to calculate the degree of the map, but one can, for example, just count the number of preimages of a generic point.
Aug 11, 2018 at 20:53	history	edited	Dmitri Panov	CC BY-SA 4.0	added 42 characters in body
Aug 11, 2018 at 20:38	history	edited	Dmitri Panov	CC BY-SA 4.0	added 45 characters in body
Aug 11, 2018 at 15:48	comment	added	Sigur		So, $\phi$ should be normalized to go into sphere, right?
Aug 9, 2018 at 23:40	comment	added	mme		Yeah, that's much better. Very simple, as it should be.
Aug 9, 2018 at 23:37	history	edited	Dmitri Panov	CC BY-SA 4.0	deleted 1 character in body
Aug 9, 2018 at 23:32	history	edited	Dmitri Panov	CC BY-SA 4.0	added 45 characters in body
Aug 9, 2018 at 23:20	history	answered	Dmitri Panov	CC BY-SA 4.0