Wall's D2 problem (Wall 1965) asks whether a finite connected CW-complex with the homological properties of a two-dimensional
CW-complex is homotopy
equivalent to a finite CW-complex of dimension
at most 2. More precisely, let 
be the CW-complex, 
its fundamental group,
and 
its universal cover. The hypotheses are
 |
for every 
,
and
 |
The second condition is required for every module 
over the group
ring ![Z[G]](/images/equations/WallsD2Problem/Inline6.svg)
.
Here the action of 
on 
supplies the coefficients for cohomology; they need
not be constant. Thus the hypotheses restrict homology
groups and cohomology, while the conclusion asks
for a finite two-dimensional model of the entire homotopy
type.
