/sci/ - Science & Math

>>12569092
Put like that, I guess I'll just
>>12568890
S
Thanks!

>>11625438
In that case, let's start with an actual sphere of some positive dimension (at least 2 if it is our base space). There is the nice fact that the only non-trivial columns (base space) or the only non-trivial rows (fibre) are the 0th and the one corresponding to the sphere's dimension. If the space in question is a homology sphere, then its (co)homology is that of a sphere of some positive dimension, and the same things apply. The only non-trivial differentials can then be the ones that reach far enough horizontally (base) or vertically (fibre).

I stumbled across a situation like this today with a space I needed to consider consisting of a bunch of cells of dimension at most 8 and one of dimension 10. Pinching the 8-skeleton to a point gave me the 10-sphere and a map from the original space into this sphere. Taking the fibre of that map, I was in the situation where the base space ended up giving me a nice 9-periodic cohomology for the fibre.

>>11625437
I wish I knew. I'd keep that stuff close to myself every day. At the moment I am animated by caffeine.