|
2
2
|
Can a Poincaré duality group $G$ contain Baumslag--Solitar subgroups $H$ such as BS(1,3) or BS(2,3)? I don't mean to include those subgroups which are the fundamental group of the torus or Klein bottle. Also, one can show that index must be infinite: $[G:H] = \infty$. If so, what is a simple example of such $G$ and $H$? In any case, please let me know of references. Thanks! |
||
|
|
|
8
|
The presentation complex of $BS(m,n)$ is aspherical (as is the presentation complex of any torsion-free 1-related group, see Lyndon and Schupp, "Combinatorial group theory", page 161). Hence by the Davis construction, $BS(m,n)$ embeds into the fundamental group of a closed aspherical 4-dim. manifold which is a PD group . An explicit presentation of that bigger group may be not easy. |
|||
|
|
