<s>
In	O
mathematics	O
,	O
the	O
principal	B-Algorithm
orbit	I-Algorithm
type	I-Algorithm
theorem	I-Algorithm
states	O
that	O
compact	O
Lie	O
group	O
acting	O
smoothly	O
on	O
a	O
connected	O
differentiable	O
manifold	B-Architecture
has	O
a	O
principal	B-Algorithm
orbit	I-Algorithm
type	I-Algorithm
.	O
</s>
<s>
Suppose	O
G	O
is	O
a	O
compact	O
Lie	O
group	O
acting	O
smoothly	O
on	O
a	O
connected	O
differentiable	O
manifold	B-Architecture
M	O
.	O
</s>
<s>
The	O
principal	B-Algorithm
orbit	I-Algorithm
type	I-Algorithm
theorem	I-Algorithm
states	O
that	O
there	O
is	O
a	O
unique	O
isotropy	O
type	O
such	O
that	O
the	O
set	O
of	O
points	O
of	O
M	O
with	O
isotropy	O
groups	O
in	O
this	O
isotropy	O
type	O
is	O
open	O
and	O
dense	O
.	O
</s>
<s>
The	O
principal	B-Algorithm
orbit	I-Algorithm
type	I-Algorithm
is	O
the	O
space	O
G/H	O
,	O
where	O
H	O
is	O
a	O
subgroup	O
in	O
the	O
isotropy	O
type	O
above	O
.	O
</s>
