# 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 $\Q$?