<s>
In	O
noncommutative	O
geometry	O
,	O
the	O
JLO	B-Algorithm
cocycle	I-Algorithm
is	O
a	O
cocycle	O
(	O
and	O
thus	O
defines	O
a	O
cohomology	O
class	O
)	O
in	O
entire	O
cyclic	O
cohomology	O
.	O
</s>
<s>
It	O
is	O
a	O
non-commutative	O
version	O
of	O
the	O
classic	O
Chern	O
character	O
of	O
the	O
conventional	O
differential	B-Language
geometry	I-Language
.	O
</s>
<s>
The	O
JLO	B-Algorithm
cocycle	I-Algorithm
is	O
associated	O
with	O
a	O
metric	O
structure	O
of	O
non-commutative	O
differential	B-Language
geometry	I-Language
known	O
as	O
a	O
-summable	O
spectral	B-Algorithm
triple	I-Algorithm
(	O
also	O
known	O
as	O
a	O
-summable	O
Fredholm	O
module	O
)	O
.	O
</s>
<s>
A	O
-summable	O
spectral	B-Algorithm
triple	I-Algorithm
consists	O
of	O
the	O
following	O
data	O
:	O
</s>
<s>
A	O
classic	O
example	O
of	O
a	O
-summable	O
spectral	B-Algorithm
triple	I-Algorithm
arises	O
as	O
follows	O
.	O
</s>
