Possible homology of closed manifolds.
2008-03-09 01:10:21 +0000 questions mathematics
In this fun paper,
MR1845679it is pointed out that
- homology is a very basic invariant, and
- closed manifolds are very basic objects
It isn't very hard to realize any sequence of abelian groups up to the middle dimension, but that middle dimension is tricky (e.g., classify $(n-1)$-connected $2n$-manifolds).
Anyway, I was wondering: is this realization question solvable for homology with coefficients in $\Z/2\Z$ or $\Q$?