An
S
L
n
SL_n
-character of a group
G
G
is the trace of an
S
L
n
SL_n
-representation of
G
.
G.
We show that all algebraic relations between
S
L
n
SL_n
-characters of
G
G
can be visualized as relations between graphs (resembling Feynman diagrams) in any topological space
X
,
X,
with
π
1
(
X
)
=
G
.
\pi _1(X)=G.
We also show that all such relations are implied by a single local relation between graphs. In this way, we provide a topological approach to the study of
S
L
n
SL_n
-representations of groups.
The motivation for this paper was our work with J. Przytycki on invariants of links in 3-manifolds which are based on the Kauffman bracket skein relation. These invariants lead to a notion of a skein module of
M
M
which, by a theorem of Bullock, Przytycki, and the author, is a deformation of the
S
L
2
SL_2
-character variety of
π
1
(
M
)
.
\pi _1(M).
This paper provides a generalization of this result to all
S
L
n
SL_n
-character varieties.