Three dimensional Heisenberg group (Ex)

Is the three dimensional Heisenberg group $\langle x,y,z \mid [x,y] = z, [x,z] = 1, [y,z] = 1\}$$<wikitex>; Is the three dimensional Heisenberg group $\langle x,y,z \mid [x,y] = z, [x,z] = 1, [y,z] = 1\}$ the fundamental group of a closed orientable $-manifold? </wikitex> [[Category:Exercises]] [[Category:Exercises with solution]]\langle x,y,z \mid [x,y] = z, [x,z] = 1, [y,z] = 1\}$ the fundamental group of a closed orientable $3$$3$-manifold?