Let M and N be closed, compact manifolds of dimension m and let X be a closed manifold of dimension
n
>
m
n > m
with embeddings of
X
×
D
m
−
n
X\, \times \,{D^{m - n}}
into M and N. Suppose the interior of
X
×
D
m
−
n
X\, \times \,{D^{m - n}}
is removed from M and N and the resulting manifolds are attached via a homeomorphism
f
:
X
×
S
m
−
n
−
1
→
X
×
S
m
−
n
−
1
f:\,X \times \,{S^{m - n - 1}}\, \to \,X\, \times \,{S^{m - n - 1}}
. Let this homeomorphism be of the form
f
(
x
,
t
)
=
(
x
,
F
(
x
)
(
t
)
)
f(x,\,t)\, = \,(x,\,F(x)(t))
where
F
:
X
→
S
O
(
m
−
n
)
F:\,X \to \,SO(m - n)
. The resulting manifold, written as
M
#
X
N
M\,{\# _X}\,N
, is called the adjacent connected sum of M and N along X. In this paper definitions and examples are given and the examples are then used to classify actions of the torus
T
n
{T^n}
on closed, compact, connected, simply connected
(
n
+
2
)
(n\, + \,2)
-manifolds,
n
⩾
4
n \geqslant \,4
.