Talk:Three dimensional Heisenberg group (Ex)
From Manifold Atlas
Let be a torus and let
and
be generators of
. Let
be a homeomorphism of the torus such that
and
(ie.
is a Dehn twist.) Let
be a torus bundle over
with monodromy
. Then
is an HNN extension of
and we can write down a presentation
, with stable letter
.
This is equivalent to the given presentation of the Heisenberg group. Therefore
is the desired closed, orientable
-manifold.